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Study of bounded analytic functions and associated operators on spaces of analytic functions

Research Project

Project/Area Number 21540166
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionNiigata University

Principal Investigator

IZUCHI Keiji  新潟大学, 自然科学系, 教授 (80120963)

Co-Investigator(Kenkyū-buntansha) HATORI Osamu  新潟大学, 自然科学系, 教授 (70156363)
OHNO Syuichi  日本工業大学, 工学部, 准教授 (20265367)
IZUCHI Kouhei  山口大学, 教育学部, 講師 (90451434)
Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords関数解析 / 複素解析 / 解析関数空間 / 有界解析関数 / ハーデイ空間 / 不変部分空間 / 閉イデアル / クロス交換子 / 合成作用素 / バナッハ環 / 界解析関数
Research Abstract

(1) It is determined the structure of closed ideals in H∞whose common zero sets are contained in the union set of nontrivial of Gleason parts in the maximal ideal space of H∞. Moreover it is proved that a countably generated closed ideal is a tensor product of simple closed ideals.(2) It is determined path connected components in the space of weighted composition operators on H∞and h∞with respect to the operator norm.(3) It is determined the rank of invariant and backward shift invariant subspaces of H^2(D^2) associated with sequences of Blaschke products.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (72 results)

All 2012 2011 2010 2009 Other

All Journal Article (44 results) (of which Peer Reviewed: 44 results) Presentation (28 results)

  • [Journal Article] Cross commutators on backward shift invariant subspaces over the bidisk II2012

    • Author(s)
      泉池敬司
    • Journal Title

      J.Korean Math.Soc.

      Volume: 49 Pages: 139-151

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Multiplicative isometries on the Smirnov class2012

    • Author(s)
      羽鳥理
    • Journal Title

      Rocky Mountain Jour.Math.

      Volume: 42 Pages: 117-150

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Multiplicative isometries on F-algebras of holomorphic functions2012

    • Author(s)
      羽鳥理
    • Journal Title

      Abstract and Applied Analysis

      Volume: 2012 Issue: 1 Pages: 1-16

    • DOI

      10.1155/2012/125987

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Isometries of the unitary groups2012

    • Author(s)
      羽鳥理
    • Journal Title

      Proc.Amer.Math.Soc.

      Volume: 140 Pages: 2141-2154

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] New criteria for equivalence of locally compact abelian groups2012

    • Author(s)
      羽鳥理
    • Journal Title

      J.Group Theory

      Volume: 15 Pages: 271-277

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Ranks of invariant subspaces of the Hardy space over the bidisk2011

    • Author(s)
      Izuchi, Kei Ji ; Izuchi, Kou Hei ; Izuchi, Yuko
    • Journal Title

      J Reine Angew. Math

      Volume: 659 Pages: 101-139

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Weighted composition operators on the space of bounded harmonic functions2011

    • Author(s)
      Izuchi, Kei Ji ; Izuchi, Yuko ; Ohno, Shuichi
    • Journal Title

      Integral Equations Operator Theory

      Volume: 71, no.1 Pages: 91-111

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Blaschke products and the rank of backward shift invariant subspaces over the bidisk2011

    • Author(s)
      Izuchi, Kei Ji ; Izuchi, Kou Hei ; Izuchi, Yuko
    • Journal Title

      J Funct. Anal

      Volume: 261, no.6 Pages: 1457-1468

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Factorization of Blaschke products andideal theory in H∞2011

    • Author(s)
      Izuchi, Kei Ji ; Izuchi, Yuko
    • Journal Title

      J Funct. Anal

      Volume: 260, no.7 Pages: 2086-2147

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Ranks of invariant subspaces of the Hardy space over the bidisk2011

    • Author(s)
      泉池敬司
    • Journal Title

      J.Reine Angew.Math.

      Volume: 659 Pages: 101-139

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Sums of weighted composition operators on H∞2011

    • Author(s)
      泉池敬司
    • Journal Title

      J.Math.Anal.Appl.

      Volume: 384 Pages: 683-689

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Weighted composition operators on the space of bounded harmonic functions2011

    • Author(s)
      泉池敬司
    • Journal Title

      Integral Equations Operator Theory

      Volume: 71 Pages: 91-111

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Blaschke products and the rank of backward shift invariant subspaces over the bidisk2011

    • Author(s)
      泉池敬司
    • Journal Title

      J.Funct.Anal.

      Volume: 261 Pages: 1457-1468

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Factorization of Blaschke products and ideal theory in H∞2011

    • Author(s)
      泉池敬司
    • Journal Title

      J.Funct.Anal.

      Volume: 260 Pages: 2086-2147

    • Related Report
      2011 Annual Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Mixed invariant subspaces over the bidisk I2011

    • Author(s)
      泉池敬司
    • Journal Title

      Complex Analysis and Operator Theory

      Volume: 5 Issue: 4 Pages: 1003-1030

    • DOI

      10.1007/s11785-009-0042-0

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Algebraic properties of isometries between groups of invertible elements in Banach algebras2011

    • Author(s)
      羽鳥理
    • Journal Title

      J.Math.Anal.Appl.

      Volume: 376 Pages: 74-83

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Spectral preservers in commutative Banach algebras2011

    • Author(s)
      羽鳥理
    • Journal Title

      Contemp.Math.

      Volume: 547 Pages: 103-123

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Multiplicative isometries on the Smirnov class2011

    • Author(s)
      羽鳥理
    • Journal Title

      Cent.Eur.J.Math.

      Volume: 9 Pages: 1051-1056

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Linear combinations of composition operators on the Bloch spaces2011

    • Author(s)
      大野修一
    • Journal Title

      Canad.J.Math.

      Volume: 63 Pages: 862-877

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Weighted composition operators from reproducing Hilbert spaces to Bloch spaces2011

    • Author(s)
      大野修一
    • Journal Title

      Houston J.Math.

      Volume: 37 Pages: 537-558

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Differences of weighted composition operators acting from Bloch space to H∞2011

    • Author(s)
      細川卓也
    • Journal Title

      Trans.Amer.Math.Soc.

      Volume: 363 Pages: 5321-5340

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Wandering subspaces and quasi-wandering subspaces in the Bergman space2011

    • Author(s)
      泉池耕平
    • Journal Title

      New York J.Math.

      Volume: 17A Pages: 301-305

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Wandering subspaces and the Beurling type Theorem I, Arch2010

    • Author(s)
      Izuchi, Kei Ji ; Izuchi, Kou Hei ; Izuchi, Yuko
    • Journal Title

      Math.(Basel)

      Volume: 95, no.5 Pages: 439-446

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Factorization of Blaschke products and primary ideals in H∞2010

    • Author(s)
      Izuchi, Kei Ji ; Izuchi, Yuko
    • Journal Title

      J Funct. Anal

      Volume: 259, no.4 Pages: 975-1013

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Wandering subspaces and the Beurling theorem I2010

    • Author(s)
      泉池敬司
    • Journal Title

      Archiv der Mathematik

      Volume: Vol.95 Pages: 439-446

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Quasi-wandering subspaces in the Bergman space2010

    • Author(s)
      泉池敬司
    • Journal Title

      Integral Equations Operator Theory

      Volume: Vol.67 Pages: 151-161

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Factorization of Blaschke products and primary ideals in H∞2010

    • Author(s)
      泉池敬司
    • Journal Title

      J.Funct.Anal

      Volume: Vol.259 Pages: 975-1013

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Ranks of cross commutators on backward shift invariant subspaces over the bidisk2010

    • Author(s)
      泉池敬司
    • Journal Title

      Rocky Mountain J.Math.

      Volume: Vol.40 Pages: 929-942

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Wandering subspaces and the Beurling type theorem II2010

    • Author(s)
      泉池敬司
    • Journal Title

      New York J.Math.

      Volume: Vol.16 Pages: 489-505

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Additively spectral-radius preserving surjections between unital semisimple commutative Banach algebras2010

    • Author(s)
      羽鳥理
    • Journal Title

      Cent.Eur.J.Math.

      Volume: Vol.8 Pages: 597-601

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generalizations of spectrally multiplicative surjections between uniform algebras2010

    • Author(s)
      羽鳥理
    • Journal Title

      Rend.Circ.Mat.Palermo

      Volume: Vol.59 Pages: 161-183

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Complete continuity of linear combinations of composition operators2010

    • Author(s)
      Nguyen, Quang Dieu
    • Journal Title

      Archiv der Mathematik

      Volume: Vol.94 Pages: 67-72

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Differences of weighted composition operators on the disk algebra2010

    • Author(s)
      大野修一
    • Journal Title

      Bulletin of the Belgian Mathematical Society - Simon Stevin

      Volume: Vol.17 Pages: 101-107

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Rank-one cross commutators on backward shift invariant subspaces on the bidisk2009

    • Author(s)
      Izuchi, Kei Ji ; Izuchi, Kou Hei
    • Journal Title

      Acta Math Sin.

      Volume: 25, no.5 Pages: 693-714

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Rank-one cross commutators on backward shift invariant subspaces on the bidisk2009

    • Author(s)
      Kei Ji Izuchi
    • Journal Title

      Acta Mathematica Sinica (Engl. Ser.) 25

      Pages: 693-714

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Equivalence classes of mixed invariant subspaces over the bidisk2009

    • Author(s)
      Kei Ji Izuchi
    • Journal Title

      Nihonkai Math. J. 20

      Pages: 145-154

    • NAID

      110007605718

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Isometries between groups of invertible elements in Banach algebras2009

    • Author(s)
      Osamu Hatori
    • Journal Title

      Studia Math. 194

      Pages: 293-304

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Peripheral multiplicativity of maps on uniformly closed algebras of continuous functions which vanish at infinity2009

    • Author(s)
      Osamu Hatori
    • Journal Title

      Tokyo J.Math. 32

      Pages: 91-104

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Stone-Weierstrass theorem for Banach function spaces satisfying a certain separation property2009

    • Author(s)
      Eggert Briem
    • Journal Title

      J.Math. Anal. Appl 353

      Pages: 607-613

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Peripherally monomial-preserving maps between uniform algebras2009

    • Author(s)
      Osamu Hatori
    • Journal Title

      Mediterr. J.Math. 6

      Pages: 47-59

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Products of differentiation and composition on Bloch spaces2009

    • Author(s)
      Syuichi Ohno
    • Journal Title

      Bull. Korean Math. Soc. 46

      Pages: 1135-1140

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Wandering subspaces and the Beurling type theorem III

    • Author(s)
      Izuchi, Kei Ji ; Izuchi, Kou Hei ; Izuchi, Yuko
    • Journal Title

      J. Math. Soc. Japan

      Volume: (to appear)

    • NAID

      10030740444

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Gleasonparts and countably generated closed ideals in H∞

    • Author(s)
      Izuchi, Kei Ji ; Izuchi, Yuko
    • Volume
      (to appear)
    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Path connected components in weighted composition operators on h∞

    • Author(s)
      Izuchi, Kei Ji ; Izuchi, Yuko ; Ohno, Shuichi
    • Journal Title

      Trans. Amer. Math. Soc.

      Volume: (to appear)

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Presentation] Weighted composition operators on the space of bounded harmonic functions2012

    • Author(s)
      泉池敬司、泉池佑子、大野修一
    • Organizer
      日本数学会
    • Place of Presentation
      東京理科大学
    • Year and Date
      2012-03-27
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [Presentation] ユニタリー群上の等距離写像2012

    • Author(s)
      羽鳥理
    • Organizer
      つくばセミナー
    • Place of Presentation
      筑波大学自然科学系
    • Year and Date
      2012-03-06
    • Related Report
      2011 Annual Research Report
  • [Presentation] Interpolations for Holder inequality2011

    • Author(s)
      泉池耕平
    • Organizer
      The 20th Seminar on Function Spaces
    • Place of Presentation
      北海道大学
    • Year and Date
      2011-12-25
    • Related Report
      2011 Annual Research Report
  • [Presentation] Criteria for the equivalence of LCA groups2011

    • Author(s)
      羽鳥理
    • Organizer
      Workshop on Commutative Algebra 2011 in Nara University of Education--Commutative Algebra and related topics--
    • Place of Presentation
      奈良教育大学
    • Year and Date
      2011-11-04
    • Related Report
      2011 Annual Research Report
  • [Presentation] Sequential properties of the maximal ideal space of H∞2011

    • Author(s)
      泉池敬司
    • Organizer
      日本数学会
    • Place of Presentation
      信州大学
    • Year and Date
      2011-09-30
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [Presentation] Blaschke products and the rank of backward shift invariant subspaces over the bidisk2011

    • Author(s)
      泉池耕平
    • Organizer
      日本数学会
    • Place of Presentation
      信州大学
    • Year and Date
      2011-09-30
    • Related Report
      2011 Final Research Report
  • [Presentation] Weighted composition operators from reproducing Hilbert spaces to Bloch spaces2011

    • Author(s)
      大野修一
    • Organizer
      日本数学会
    • Place of Presentation
      信州大学
    • Year and Date
      2011-09-30
    • Related Report
      2011 Annual Research Report
  • [Presentation] Differences of weighted composition operators on the diskalgebra2011

    • Author(s)
      大野修一
    • Organizer
      日本数学会
    • Place of Presentation
      信州大学
    • Year and Date
      2011-09-30
    • Related Report
      2011 Annual Research Report
  • [Presentation] Blaschke products and the rank of backward shift invariant Subspaces over the bidisk2011

    • Author(s)
      泉池耕平
    • Organizer
      日本数学会
    • Place of Presentation
      信州大学
    • Year and Date
      2011-09-30
    • Related Report
      2011 Annual Research Report
  • [Presentation] Gleason部分に関連するの閉イデアルの構造2011

    • Author(s)
      泉池敬司
    • Organizer
      第50回実函数論・函数解析学合同シンポジュウム
    • Place of Presentation
      東京女子大
    • Year and Date
      2011-08-09
    • Related Report
      2011 Final Research Report
  • [Presentation] Gleason部分に関連するH(∞)の閉イデアルの構造2011

    • Author(s)
      泉池敬司
    • Organizer
      第50回実函数論・函数解析学合同シンポジュウム
    • Place of Presentation
      東京女子大(招待講演)
    • Year and Date
      2011-08-09
    • Related Report
      2011 Annual Research Report
  • [Presentation] LCA群の同形性と測度環における等距離性2011

    • Author(s)
      羽鳥理
    • Organizer
      つくばセミナー
    • Place of Presentation
      筑波大学
    • Year and Date
      2011-03-08
    • Related Report
      2010 Annual Research Report
  • [Presentation] Weighted composition operators from Bloch spaces to Hardy spaces2011

    • Author(s)
      大野修一
    • Organizer
      The 19th Miyashiro Seminar
    • Place of Presentation
      日本工業大学
    • Year and Date
      2011-01-09
    • Related Report
      2010 Annual Research Report
  • [Presentation] Wandering subspaces and the Beurling type theorem2010

    • Author(s)
      泉池敬司
    • Organizer
      第19回関数空間セミナー
    • Place of Presentation
      北海道大学
    • Year and Date
      2010-12-25
    • Related Report
      2010 Annual Research Report
  • [Presentation] Algebraic structures of isometries on groups2010

    • Author(s)
      羽鳥理
    • Organizer
      The Sixth Conference on Function Spaces
    • Place of Presentation
      Southern Illinois University
    • Year and Date
      2010-12-25
    • Related Report
      2010 Annual Research Report
  • [Presentation] Wandering subspaces and the Beurling type theorem2010

    • Author(s)
      泉池敬司
    • Organizer
      The 13^<th> Conference on Real and Complex Analysis in Hiroshima
    • Place of Presentation
      広島大学
    • Year and Date
      2010-12-20
    • Related Report
      2010 Annual Research Report
  • [Presentation] Non-linear isometries on the Smirnov class2010

    • Author(s)
      r飯田安保
    • Organizer
      2010年度関数環研究集会
    • Place of Presentation
      信州大学
    • Year and Date
      2010-11-29
    • Related Report
      2010 Annual Research Report
  • [Presentation] 等距離写像の代数構造2010

    • Author(s)
      羽鳥理
    • Organizer
      2010年度関数環研究集会
    • Place of Presentation
      信州大学
    • Year and Date
      2010-11-29
    • Related Report
      2010 Annual Research Report
  • [Presentation] Factorization of Blaschke products and primary ideals in H∞2010

    • Author(s)
      泉池敬司、泉池佑子
    • Organizer
      日本数学会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-25
    • Related Report
      2011 Final Research Report
  • [Presentation] Factorization of Blaschke products and primary ideals in H∞2010

    • Author(s)
      泉池敬司
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-25
    • Related Report
      2010 Annual Research Report
  • [Presentation] Products of differentiation and composition on Bloch spaces2010

    • Author(s)
      大野修一
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-25
    • Related Report
      2010 Annual Research Report
  • [Presentation] Complete continuity of linear combinations of composition operators2010

    • Author(s)
      Nguyen, Quang Dieu
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-25
    • Related Report
      2010 Annual Research Report
  • [Presentation] コンパクトLie群上の等距離写像2010

    • Author(s)
      羽鳥理
    • Organizer
      高橋眞映先生御退職記念研究集会
    • Place of Presentation
      山形大学
    • Year and Date
      2010-06-26
    • Related Report
      2010 Annual Research Report
  • [Presentation] The reproducing Hilbert spaces2010

    • Author(s)
      大野修一
    • Organizer
      可換Banach環と種々の分野との交流 III
    • Place of Presentation
      山形大学
    • Year and Date
      2010-06-26
    • Related Report
      2010 Annual Research Report
  • [Presentation] Composition operators induced by analytic maps from a unit disk to a polydisk2010

    • Author(s)
      大野修一
    • Organizer
      The 18th Miyashiro Seminar
    • Place of Presentation
      日本工業大学
    • Year and Date
      2010-06-19
    • Related Report
      2010 Annual Research Report
  • [Presentation] Ranks of invariant subspaces of the Hardy space over the bidisk2009

    • Author(s)
      Keiji Izuchi
    • Organizer
      Joint Meeting of the KMS and the AMS
    • Place of Presentation
      梨花女子大、韓国
    • Year and Date
      2009-12-17
    • Related Report
      2009 Annual Research Report
  • [Presentation] Composition operators on the space of bounded harmonic functions2009

    • Author(s)
      大野修一
    • Organizer
      日本数学会賞秋季総合分科会
    • Place of Presentation
      大阪大学豊中キャンパス
    • Year and Date
      2009-09-26
    • Related Report
      2009 Annual Research Report
  • [Presentation] Characterization of mixed invariant subspaces on the torus2009

    • Author(s)
      内藤雅俊
    • Organizer
      日本数学会賞秋季総合分科会
    • Place of Presentation
      大阪大学豊中キャンパス
    • Year and Date
      2009-09-26
    • Related Report
      2009 Annual Research Report

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Published: 2009-04-01   Modified: 2016-04-21  

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