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Study of operators on spaces of analytic functions and the space of bounded analytic functions

Research Project

Project/Area Number 24540164
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionNiigata University

Principal Investigator

IZUCHI Keiji  新潟大学, 自然科学系, フェロ- (80120963)

Co-Investigator(Kenkyū-buntansha) OHNO Syuichi  日本工業大学, 工学部, 准教授 (20265367)
HATORI Osamu  新潟大学, 自然科学系, 教授 (70156363)
IZUCHI Kouhei  山口大学, 教育学部, 講師 (90451434)
Project Period (FY) 2012-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2012: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywords有界解析関数 / 極大イデアル空間 / 閉イデアル / ハーデイ空間 / 不変部分空間 / 内部関数 / 荷重合成作用素 / 弧状連結成分 / 有界解析関数空間 / 有界調和関数空間 / 作用素ノルム位相 / 本質作用素ノルム位相 / 多変数ハーデイ空間 / 合成作用素の連結成分 / 国際研究者交流:フィンランド / 国際情報交換:中国 / 国際情報交換:韓国
Outline of Final Research Achievements

It is determined the structure of closed ideals and countably generated closed ideals whose common zero sets in the maximal ideal space of the Banach algebra of bounded analytic functions on the open unit disk are contained in the union set of nontrivial Gleason parts. It is also determined the path connected components of the weighted composition operators on the space of bounded analytic functions with respect to the operator norm and essential operator norm topologies. Moreover the path connected components are determined on the space of bounded harmonic functions and on the disk algebra.
The study of the Hardy space on the bidisk, some backward shift invariant subspaces having rank 1 cross commutator are described. It is also determined the ranks of Rudin type (backward) shift invariant subspaces associated with sequences of inner functions satisfying some conditions,

Report

(4 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (62 results)

All 2015 2014 2013 2012 Other

All Journal Article (42 results) (of which Peer Reviewed: 42 results,  Acknowledgement Compliant: 11 results,  Open Access: 8 results) Presentation (20 results) (of which Invited: 3 results)

  • [Journal Article] Inner functions and weighted composition operators on the Hardy-Hilbert space with the unbounded weights.2015

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

      Ann. Funct. Anal.

      Volume: 6 Pages: 104-115

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Weighted composition operators between Hilbert spaces of analytic functions in the operator norm and Hilbert-Schmidt norm topologies.2015

    • Author(s)
      Takuya Hosokawa, Kei Ji Izuchi, Shuichi Ohno
    • Journal Title

      J. Math. Anal. Appl.

      Volume: 421 Pages: 1546-1558

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Weighted composition operators on H∞・B_o.2015

    • Author(s)
      Shuichi Ohno
    • Journal Title

      Glasgow Math. J.

      Volume: 57 Issue: 2 Pages: 475-480

    • DOI

      10.1017/s0017089514000469

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Topological structure of the space of weighted composition operators between different Hardy spaces.2014

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

      Integral Equations Operator Theory

      Volume: 80 Pages: 153-164

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Path connected components in weighted composition operators on h∞ and H∞ with the essential operator norm.2014

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

      Houston J. Math.

      Volume: 40 Pages: 161-187

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Boundary vs. interior conditions associated with weighted composition operators.2014

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

      Cent. Eur. J. Math.

      Volume: 12 Pages: 761-777

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Composition operators related to the Dirichlet space.2014

    • Author(s)
      Shuichi Ohno
    • Journal Title

      Bulletin of the Belgian Mathematical Society - Simon Stevin

      Volume: 21

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Weighted composition operators on the minimal Mobius invariant space.2014

    • Author(s)
      Shuichi Ohno
    • Journal Title

      Bull. Korean Math. Soc.

      Volume: 51 Issue: 4 Pages: 1187-1193

    • DOI

      10.4134/bkms.2014.51.4.1187

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Isometries of the unitary groups in C*-algebras.2014

    • Author(s)
      Osamu Hatori
    • Journal Title

      Studia Math.

      Volume: 221 Pages: 61-86

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Maps which preserve norms of non-symmetrical quotients between groups of exponentials of Lipschitz functions.2014

    • Author(s)
      Osamu Hatori, A. Jimenez-Vargas, Moises Villegas-Vallecillos
    • Journal Title

      J. Math. Anal. Appl.

      Volume: 415 Pages: 825-845

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Isometries of the unitary groups and Thompson isometries of the spaces of invertible positive elements in C*-algebras.2014

    • Author(s)
      Osamu Hatori, Lajos Molnar
    • Journal Title

      J. Math. Anal. Appl.

      Volume: 409 Pages: 158-167

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Isometries of the unitary groups and Thompson isometries of the spaces of invertible positive elements in C*-algebras.2014

    • Author(s)
      Osamu Hatori; Lajos Molnar
    • Journal Title

      J. Math. Anal. Appl.

      Volume: 409

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Sequential properties of the maximal ideal space of H∞ .2013

    • Author(s)
      Keiji Izuchi; Yuko Izuchi
    • Journal Title

      Houston J. Math.

      Volume: 39

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Mixed invariant subspaces over the bidisk II.2013

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

      Acta Math. Vietnam.

      Volume: 38

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Ranks of backward shift invariant subspaces of the Hardy space over the bidisk.2013

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

      Math. Z.

      Volume: 274

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Gleason parts and countably generated closed ideals in H∞.2013

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

      Trans. Amer. Math. Soc.

      Volume: 365

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Interpolations for Holder's inequality.2013

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

      Bull. Korean Math. Soc.

      Volume: 50

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] On Mortini's question concerning the level sets on M(H∞) of a certain harmonic function.2013

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

      Topology Appl.

      Volume: 160 Pages: 1099-1101

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Path connected components in weighted composition operators on h∞ and H∞ with the operator norm.2013

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

      Trans. Amer. Math. Soc.

      Volume: 365 Pages: 3593-3612

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Essential norms of linear combinations of composition operators on h∞ .2013

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

      J. Korean Math. Soc.

      Volume: 50

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Non-analytic sets and QC-level sets in the maximal ideal space of H∞ .2013

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

      Complex Var. Elliptic Equ.

      Volume: 58

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Sums of weighted composition operators on COP.2013

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

      Glasg. Math. J.

      Volume: 55

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Real linear isometries between function algebras II.2013

    • Author(s)
      Osamu Hatori; Takeshi Miura
    • Journal Title

      Cent. Eur. J. Math.

      Volume: 11

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Isometries of the special orthogonal group.2013

    • Author(s)
      Toshikazu Abe; Shigeki Akiyama; Osamu Hatori
    • Journal Title

      Linear Algebra Appl.

      Volume: 439

    • NAID

      120007136918

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Hardy-Carleson measures and their dual Poisson-Szego transforms.2013

    • Author(s)
      Boo Rim Choe; Kou Hei Izuchi; Hyungwoon Koo
    • Journal Title

      Potential Anal.

      Volume: 38

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Sums of weighted composition operators on COP2013

    • Author(s)
      Keiji Izuchi, Kouhei Izuchi, Yuko Izuchi
    • Journal Title

      Glasgow Math. J.

      Volume: 55

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Non-analytic sets and QC-level sets in the maximal ideal space of H∞2013

    • Author(s)
      Keiji Izuchi, Yuko Izuchi
    • Journal Title

      Complex Var. Elliptic Equ.

      Volume: 58

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Gleason parts and countably generated closed ideals in H∞2013

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

      Trans. Amer. Math. Soc.

      Volume: 未定

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Ranks of backward shift invariant subspaces of the Hardy space over the bidisk2013

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

      Math. Zeit.

      Volume: 未定

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Path connected components in weighted composition operators on h∞ and H∞ with the operator norm2013

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

      Trans. Amer. Math. Soc.

      Volume: 未定

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Path connected components in weighted composition operators on h∞ and H∞ with the essential operator norm2013

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

      Houston J. Math.

      Volume: 未定

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Mutually prime sequences of inner functions and the ranks of subspaces over the bidisk2012

    • Author(s)
      Keiji Izuchi, Kouhei Izuchi, Yuko Izuchi
    • Journal Title

      Arch. Math. (Basel)

      Volume: 98

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Wandering subspaces and the Beurling type theorem III2012

    • Author(s)
      Keiji Izuchi, Kouhei Izuchi, Yuko Izuchi
    • Journal Title

      J. Math. Soc. Japan

      Volume: 64

    • NAID

      10030740444

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Cross commutators on backward shift invariant subspaces over the bidisk II2012

    • Author(s)
      Keiji Izuchi, Kouhei Izuchi
    • Journal Title

      J. Korean Math. Soc.

      Volume: 49

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Commutativity in two-variable Jordan blocks on the Hardy space2012

    • Author(s)
      Keiji Izuchi, Kouhei Izuchi
    • Journal Title

      Acta Sci. Math. (Szeged)

      Volume: 78

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Composition operators induced by analytic maps to the polydisk2012

    • Author(s)
      Keiji Izuchi, Quang Dieu Nguyen, Shuichi Ohno
    • Journal Title

      Canad. J. Math.

      Volume: 64

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Differences of Weighted Composition Operators from H∞ to Bloch space2012

    • Author(s)
      Takuya Hosokawa, Shuichi Ohno
    • Journal Title

      Taiwanese J. Math.

      Volume: 16

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Reflections and a generalization of the Mazur-Ulam theorem2012

    • Author(s)
      Osamu Hatori, Kiyotaka Kobayashi, Takeshi Miura, Sin-Ei Takahasi
    • Journal Title

      Rocky Moutain J. Math.

      Volume: 42

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Isometries of the unitary group2012

    • Author(s)
      Osamu Hatori and Lajos Molnar
    • Journal Title

      Proc. Amer. Math. Soc.

      Volume: 142

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] New criteria for equivalence of locally compact abelian groups2012

    • Author(s)
      Osamu Hatori
    • Journal Title

      J. Group Theory

      Volume: 15

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Isometries between groups of invertible elements in C*-algebras2012

    • Author(s)
      Osamu Hatori, Keiichi Watanabe
    • Journal Title

      Studia Math.

      Volume: 209

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Isometries and maps compatible with inverted Jordan triple products on groups2012

    • Author(s)
      Osamu Hatori, Go Hirasawa, Takeshi Miura, Lajos Molnar
    • Journal Title

      Tokyo J. Math.

      Volume: 135

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] Weighted composition operators on the minimal Mobius invariant space.2015

    • Author(s)
      大 野 修 一
    • Organizer
      日本数学会年会
    • Place of Presentation
      明治大学(東京都・千代田区)
    • Year and Date
      2015-03-22
    • Related Report
      2014 Annual Research Report
  • [Presentation] Topological structure of the space of weighted composition operators between different Hardy spaces.2014

    • Author(s)
      泉池敬司, 大野修一
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      広島大学(広島県・東広島市)
    • Year and Date
      2014-09-27
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Composition operators related to the Dirichlet space.2014

    • Author(s)
      大 野 修 一
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      広島大学(広島県・東広島市)
    • Year and Date
      2014-09-27
    • Related Report
      2014 Annual Research Report
  • [Presentation] Ranks of backward shift invariant subspaces of Hardy space over the bidisk.2014

    • Author(s)
      泉 池 耕 平
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      広島大学(広島県・東広島市)
    • Year and Date
      2014-09-27
    • Related Report
      2014 Annual Research Report
  • [Presentation] SO(4) 上のある写像について2014

    • Author(s)
      羽鳥 理
    • Organizer
      関数環研究集会
    • Place of Presentation
      早稲田大学(東京都・新宿区)
    • Year and Date
      2014-09-19
    • Related Report
      2014 Annual Research Report
  • [Presentation] Weighted composition operator whose ranges contain the disk algebra.2014

    • Author(s)
      泉池 敬司
    • Organizer
      関数環研究集会
    • Place of Presentation
      早稲田大学(東京都・新宿区)
    • Year and Date
      2014-09-18
    • Related Report
      2014 Annual Research Report
  • [Presentation] Path connected components in the space of weighted composition operators on the disk algebra.

    • Author(s)
      泉池敬司; 泉池佑子; 大野修一
    • Organizer
      日本数学会
    • Place of Presentation
      学習院大学、豊島区
    • Related Report
      2013 Research-status Report
  • [Presentation] Differences of weighted composition operators from H1 to the Bloch space.

    • Author(s)
      細川卓也; 大野修一
    • Organizer
      日本数学会
    • Place of Presentation
      愛媛大学、松山市
    • Related Report
      2013 Research-status Report
  • [Presentation] Operator inner functions for Rudin type invariant subspaces over the bidisk.

    • Author(s)
      泉池耕平
    • Organizer
      日本数学会
    • Place of Presentation
      愛媛大学、松山市
    • Related Report
      2013 Research-status Report
  • [Presentation] Weighted Bergman spaces embedded in the Hardy space over the bidisk.

    • Author(s)
      泉池 敬司
    • Organizer
      関数環研究集会
    • Place of Presentation
      クロスパルにいがた生涯学習センター、新潟市
    • Related Report
      2013 Research-status Report
  • [Presentation] exp A 上の preserver problem について.

    • Author(s)
      羽鳥 理
    • Organizer
      関数環研究集会
    • Place of Presentation
      クロスパルにいがた生涯学習センター、新潟市
    • Related Report
      2013 Research-status Report
  • [Presentation] Ranks of invariant and backward shift invariant subspaces of the Hardy space over the bidisk

    • Author(s)
      Keiji Izuchi
    • Organizer
      Topology and Functional Analysis
    • Place of Presentation
      Fudan University、中国
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Sums of Weighted Composition Operators on H∞

    • Author(s)
      泉池 敬司, 大野修一
    • Organizer
      日本数学会、函数解析学分科会
    • Place of Presentation
      九州大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Interpolations for H¨older’s inequality

    • Author(s)
      泉池 敬司
    • Organizer
      実解析学セミナー 2012
    • Place of Presentation
      茨城大学
    • Related Report
      2012 Research-status Report
  • [Presentation] An example of an invariant subspace M such that zM+wM is not closed

    • Author(s)
      泉池 敬司
    • Organizer
      解析学セミナー
    • Place of Presentation
      新潟大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Composition Operators Induced by Analytic Maps to the Polydisk

    • Author(s)
      泉池 敬司. Quang Dieu Nguyen, 大野修一
    • Organizer
      日本数学会、函数解析学分科会
    • Place of Presentation
      京都大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Differences of Weighted Composition Operators from the Bloch Space to H∞

    • Author(s)
      細川 卓也, 大野修一
    • Organizer
      日本数学会、函数解析学分科会
    • Place of Presentation
      九州大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Topological Structure of the Space of Weighted Composition Operators on H∞

    • Author(s)
      大野修一
    • Organizer
      日本数学会、函数解析学分科会
    • Place of Presentation
      九州大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Isometries on the unitary groups

    • Author(s)
      Osamu Hatori
    • Organizer
      Conference on Mathematics and Statistics
    • Place of Presentation
      University of Memphis
    • Related Report
      2012 Research-status Report
  • [Presentation] Mazur-Ulamの定理の非可換化とその応用

    • Author(s)
      羽鳥 理
    • Organizer
      解析学セミナー
    • Place of Presentation
      新潟大学
    • Related Report
      2012 Research-status Report

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Published: 2013-05-31   Modified: 2019-07-29  

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