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

• Project/Area Number: 21540166
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Niigata 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: ¥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.

Research Products

• [Journal Article] Cross commutators on backward shift invariant subspaces over the bidisk II (2012)
  • Author(s): 泉池敬司
  • Journal Title: J.Korean Math.Soc. Volume: 49 Pages: 139-151
  • Peer Reviewed
• [Journal Article] Multiplicative isometries on the Smirnov class (2012)
  • Author(s): 羽鳥理
  • Journal Title: Rocky Mountain Jour.Math. Volume: 42 Pages: 117-150
  • Peer Reviewed
• [Journal Article] Multiplicative isometries on F-algebras of holomorphic functions (2012)
  • Author(s): 羽鳥理
  • Journal Title: Abstract and Applied Analysis Volume: 2012 Issue: 1 Pages: 1-16
  • DOI: 10.1155/2012/125987
  • Peer Reviewed
• [Journal Article] Isometries of the unitary groups (2012)
  • Author(s): 羽鳥理
  • Journal Title: Proc.Amer.Math.Soc. Volume: 140 Pages: 2141-2154
  • Peer Reviewed
• [Journal Article] New criteria for equivalence of locally compact abelian groups (2012)
  • Author(s): 羽鳥理
  • Journal Title: J.Group Theory Volume: 15 Pages: 271-277
  • Peer Reviewed
• [Journal Article] Ranks of invariant subspaces of the Hardy space over the bidisk (2011)
  • Author(s): Izuchi, Kei Ji ; Izuchi, Kou Hei ; Izuchi, Yuko
  • Journal Title: J Reine Angew. Math Volume: 659 Pages: 101-139
  • Peer Reviewed
• [Journal Article] Weighted composition operators on the space of bounded harmonic functions (2011)
  • Author(s): Izuchi, Kei Ji ; Izuchi, Yuko ; Ohno, Shuichi
  • Journal Title: Integral Equations Operator Theory Volume: 71, no.1 Pages: 91-111
  • Peer Reviewed
• [Journal Article] Blaschke products and the rank of backward shift invariant subspaces over the bidisk (2011)
  • Author(s): Izuchi, Kei Ji ; Izuchi, Kou Hei ; Izuchi, Yuko
  • Journal Title: J Funct. Anal Volume: 261, no.6 Pages: 1457-1468
  • 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
  • Peer Reviewed
• [Journal Article] Ranks of invariant subspaces of the Hardy space over the bidisk (2011)
  • Author(s): 泉池敬司
  • Journal Title: J.Reine Angew.Math. Volume: 659 Pages: 101-139
  • 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
  • Peer Reviewed
• [Journal Article] Weighted composition operators on the space of bounded harmonic functions (2011)
  • Author(s): 泉池敬司
  • Journal Title: Integral Equations Operator Theory Volume: 71 Pages: 91-111
  • Peer Reviewed
• [Journal Article] Blaschke products and the rank of backward shift invariant subspaces over the bidisk (2011)
  • Author(s): 泉池敬司
  • Journal Title: J.Funct.Anal. Volume: 261 Pages: 1457-1468
  • 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
  • Peer Reviewed
• [Journal Article] Mixed invariant subspaces over the bidisk I (2011)
  • 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
  • Peer Reviewed
• [Journal Article] Algebraic properties of isometries between groups of invertible elements in Banach algebras (2011)
  • Author(s): 羽鳥理
  • Journal Title: J.Math.Anal.Appl. Volume: 376 Pages: 74-83
  • Peer Reviewed
• [Journal Article] Spectral preservers in commutative Banach algebras (2011)
  • Author(s): 羽鳥理
  • Journal Title: Contemp.Math. Volume: 547 Pages: 103-123
  • Peer Reviewed
• [Journal Article] Multiplicative isometries on the Smirnov class (2011)
  • Author(s): 羽鳥理
  • Journal Title: Cent.Eur.J.Math. Volume: 9 Pages: 1051-1056
  • Peer Reviewed
• [Journal Article] Linear combinations of composition operators on the Bloch spaces (2011)
  • Author(s): 大野修一
  • Journal Title: Canad.J.Math. Volume: 63 Pages: 862-877
  • Peer Reviewed
• [Journal Article] Weighted composition operators from reproducing Hilbert spaces to Bloch spaces (2011)
  • Author(s): 大野修一
  • Journal Title: Houston J.Math. Volume: 37 Pages: 537-558
  • 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
  • Peer Reviewed
• [Journal Article] Wandering subspaces and quasi-wandering subspaces in the Bergman space (2011)
  • Author(s): 泉池耕平
  • Journal Title: New York J.Math. Volume: 17A Pages: 301-305
  • Peer Reviewed
• [Journal Article] Wandering subspaces and the Beurling type Theorem I, Arch (2010)
  • Author(s): Izuchi, Kei Ji ; Izuchi, Kou Hei ; Izuchi, Yuko
  • Journal Title: Math.(Basel) Volume: 95, no.5 Pages: 439-446
  • 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
  • Peer Reviewed
• [Journal Article] Wandering subspaces and the Beurling theorem I (2010)
  • Author(s): 泉池敬司
  • Journal Title: Archiv der Mathematik Volume: Vol.95 Pages: 439-446
  • Peer Reviewed
• [Journal Article] Quasi-wandering subspaces in the Bergman space (2010)
  • Author(s): 泉池敬司
  • Journal Title: Integral Equations Operator Theory Volume: Vol.67 Pages: 151-161
  • 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
  • Peer Reviewed
• [Journal Article] Ranks of cross commutators on backward shift invariant subspaces over the bidisk (2010)
  • Author(s): 泉池敬司
  • Journal Title: Rocky Mountain J.Math. Volume: Vol.40 Pages: 929-942
  • Peer Reviewed
• [Journal Article] Wandering subspaces and the Beurling type theorem II (2010)
  • Author(s): 泉池敬司
  • Journal Title: New York J.Math. Volume: Vol.16 Pages: 489-505
  • Peer Reviewed
• [Journal Article] Additively spectral-radius preserving surjections between unital semisimple commutative Banach algebras (2010)
  • Author(s): 羽鳥理
  • Journal Title: Cent.Eur.J.Math. Volume: Vol.8 Pages: 597-601
  • Peer Reviewed
• [Journal Article] Generalizations of spectrally multiplicative surjections between uniform algebras (2010)
  • Author(s): 羽鳥理
  • Journal Title: Rend.Circ.Mat.Palermo Volume: Vol.59 Pages: 161-183
  • Peer Reviewed
• [Journal Article] Complete continuity of linear combinations of composition operators (2010)
  • Author(s): Nguyen, Quang Dieu
  • Journal Title: Archiv der Mathematik Volume: Vol.94 Pages: 67-72
  • Peer Reviewed
• [Journal Article] Differences of weighted composition operators on the disk algebra (2010)
  • Author(s): 大野修一
  • Journal Title: Bulletin of the Belgian Mathematical Society - Simon Stevin Volume: Vol.17 Pages: 101-107
  • Peer Reviewed
• [Journal Article] Rank-one cross commutators on backward shift invariant subspaces on the bidisk (2009)
  • Author(s): Izuchi, Kei Ji ; Izuchi, Kou Hei
  • Journal Title: Acta Math Sin. Volume: 25, no.5 Pages: 693-714
  • Peer Reviewed
• [Journal Article] Rank-one cross commutators on backward shift invariant subspaces on the bidisk (2009)
  • Author(s): Kei Ji Izuchi
  • Journal Title: Acta Mathematica Sinica (Engl. Ser.) 25 Pages: 693-714
  • Peer Reviewed
• [Journal Article] Equivalence classes of mixed invariant subspaces over the bidisk (2009)
  • Author(s): Kei Ji Izuchi
  • Journal Title: Nihonkai Math. J. 20 Pages: 145-154
  • NAID: 110007605718
  • Peer Reviewed
• [Journal Article] Isometries between groups of invertible elements in Banach algebras (2009)
  • Author(s): Osamu Hatori
  • Journal Title: Studia Math. 194 Pages: 293-304
  • Peer Reviewed
• [Journal Article] Peripheral multiplicativity of maps on uniformly closed algebras of continuous functions which vanish at infinity (2009)
  • Author(s): Osamu Hatori
  • Journal Title: Tokyo J.Math. 32 Pages: 91-104
  • Peer Reviewed
• [Journal Article] A Stone-Weierstrass theorem for Banach function spaces satisfying a certain separation property (2009)
  • Author(s): Eggert Briem
  • Journal Title: J.Math. Anal. Appl 353 Pages: 607-613
  • Peer Reviewed
• [Journal Article] Peripherally monomial-preserving maps between uniform algebras (2009)
  • Author(s): Osamu Hatori
  • Journal Title: Mediterr. J.Math. 6 Pages: 47-59
  • Peer Reviewed
• [Journal Article] Products of differentiation and composition on Bloch spaces (2009)
  • Author(s): Syuichi Ohno
  • Journal Title: Bull. Korean Math. Soc. 46 Pages: 1135-1140
  • 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
  • Peer Reviewed
• [Journal Article] Gleasonparts and countably generated closed ideals in H∞
  • Author(s): Izuchi, Kei Ji ; Izuchi, Yuko
  • Volume: (to appear)
  • 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)
  • Peer Reviewed
• [Presentation] Weighted composition operators on the space of bounded harmonic functions (2012)
  • 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
• [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
• [Presentation] Interpolations for Holder inequality (2011)
  • 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
• [Presentation] Criteria for the equivalence of LCA groups (2011)
  • 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
• [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
• [Presentation] Blaschke products and the rank of backward shift invariant subspaces over the bidisk (2011)
  • 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
• [Presentation] Weighted composition operators from reproducing Hilbert spaces to Bloch spaces (2011)
  • 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
• [Presentation] Differences of weighted composition operators on the diskalgebra (2011)
  • 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
• [Presentation] Blaschke products and the rank of backward shift invariant Subspaces over the bidisk (2011)
  • 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
• [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
• [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
• [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
• [Presentation] Weighted composition operators from Bloch spaces to Hardy spaces (2011)
  • 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
• [Presentation] Wandering subspaces and the Beurling type theorem (2010)
  • 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
• [Presentation] Algebraic structures of isometries on groups (2010)
  • Author(s): 羽鳥理
  • Organizer: The Sixth Conference on Function Spaces
  • Place of Presentation: Southern Illinois University
  • Year and Date: 2010-12-25
• [Presentation] Wandering subspaces and the Beurling type theorem (2010)
  • 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
• [Presentation] Non-linear isometries on the Smirnov class (2010)
  • 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
• [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
• [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
• [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
• [Presentation] Products of differentiation and composition on Bloch spaces (2010)
  • 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
• [Presentation] Complete continuity of linear combinations of composition operators (2010)
  • 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
• [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
• [Presentation] The reproducing Hilbert spaces (2010)
  • 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
• [Presentation] Composition operators induced by analytic maps from a unit disk to a polydisk (2010)
  • 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
• [Presentation] Ranks of invariant subspaces of the Hardy space over the bidisk (2009)
  • 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
• [Presentation] Composition operators on the space of bounded harmonic functions (2009)
  • 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
• [Presentation] Characterization of mixed invariant subspaces on the torus (2009)
  • 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