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Noncommutative analysis based on operator algebras

Research Project

Project/Area Number 18H01122
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Review Section Basic Section 12010:Basic analysis-related
Research InstitutionNagoya University

Principal Investigator

Ueda Yoshimichi  名古屋大学, 多元数理科学研究科, 教授 (00314724)

Project Period (FY) 2018-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥10,140,000 (Direct Cost: ¥7,800,000、Indirect Cost: ¥2,340,000)
Fiscal Year 2022: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2021: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2020: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2019: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2018: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Keywordsランダム行列 / 大偏差原理 / 量子群 / ユニタリ表現論 / 作用素 / 関数計算 / 非可換Lp空間 / 量子ダイバージェンス / C*-環 / フォンノイマン環 / 自由確率解析 / 作用素環 / 自由確率論 / 表現 / ユニタリ球表現論 / リンク / 行列解析 / 確率測度 / 調和解析 / 帰納極限 / ユニタリ表現 / 作用素二項演算 / 作用素遠近法 / 作用素関数計算 / 非可換解析 / 行列値確率過程 / 自由独立 / 流れ / 単位的正写像 / 境界定理 / Poisson 境界 / 非可換 / エルゴード理論 / 離散群
Outline of Final Research Achievements

I worked out the random matrix model for liberation process that I introduced and studied before, and the consequence is that many problems concerning the relationship between orbital free entropy and free mutual information are reduced to the full large deviation principle for the random matrix model. I introduced a rather general framework including the spherical representation theory for inductive limits of compact quantum groups and gave its basic theory. I also gave a thorough theory for 2-variable functional calculus for Hilbert space operators. Additionally, I did various studies in non-commutative analysis.

Academic Significance and Societal Importance of the Research Achievements

非可換解析学はさまざまな意味で受け取り得るが,ヒルベルト空間上の作用素が何らかの形で関わる解析学的問題を作用素環論を踏まえつつ,作用素環論の外部に広がった形で研究を遂行した.自由化過程のランダム行列モデルは新奇なものであり,さまざまな発展が期待できる.また,球表現に関わる研究はここまで徹底した量子群の帰納極限を扱うのに使える枠組みはこれまでに与えておらず,出発点になりうるだろう.さらに2変数の関数計算の研究は基礎中の基礎というべきものなので,これまで散発的な研究で無駄が多かった部分を交通整理しており,近年の量子情報理論での利用を見るとその有用性は明らかと思われる.

Report

(6 results)
  • 2023 Final Research Report ( PDF )
  • 2022 Annual Research Report
  • 2021 Annual Research Report
  • 2020 Annual Research Report
  • 2019 Annual Research Report
  • 2018 Annual Research Report
  • Research Products

    (23 results)

All 2024 2023 2022 2021 2020 2019 Other

All Journal Article (10 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 10 results,  Open Access: 2 results) Presentation (9 results) (of which Int'l Joint Research: 2 results,  Invited: 9 results) Remarks (4 results)

  • [Journal Article] A remark on non-commutative $L^p$-spaces2024

    • Author(s)
      Kato Shinya、Ueda Yoshimichi
    • Journal Title

      Studia Mathematica

      Volume: - Issue: 3 Pages: 235-248

    • DOI

      10.4064/sm230724-11-10

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed
  • [Journal Article] SPHERICAL REPRESENTATIONS FOR -FLOWS III: WEIGHT-EXTENDED BRANCHING GRAPHS2024

    • Author(s)
      UEDA YOSHIMICHI
    • Journal Title

      Journal of the Australian Mathematical Society

      Volume: - Issue: 2 Pages: 1-34

    • DOI

      10.1017/s1446788724000053

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Lebesgue decomposition for positive operators revisited2023

    • Author(s)
      Yoshiki Aibara and Yoshimichi Ueda
    • Journal Title

      C. R. Math. Rep. Acad. Sci. Canada

      Volume: 45 Pages: 37-55

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Spherical Representations of C*-Flows II: Representation System and Quantum Group Setup2022

    • Author(s)
      Ueda Yoshimichi
    • Journal Title

      Symmetry, Integrability and Geometry: Methods and Applications

      Volume: -

    • DOI

      10.3842/sigma.2022.050

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Pusz--Woronowicz Functional Calculus and Extended Operator Convex Perspectives2021

    • Author(s)
      Hiai Fumio、Ueda Yoshimichi、Wada Shuhei
    • Journal Title

      Integral Equations and Operator Theory

      Volume: 94 Issue: 1

    • DOI

      10.1007/s00020-021-02676-y

    • Related Report
      2021 Annual Research Report 2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Pusz--Woronowicz's functional calculus revisited2021

    • Author(s)
      Hatano Kanae、Ueda Yoshimichi
    • Journal Title

      Acta Scientiarum Mathematicarum

      Volume: 87 Issue: 3-4 Pages: 485-503

    • DOI

      10.14232/actasm-021-263-6

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Matrix Liberation Process II: Relation to Orbital Free Entropy2020

    • Author(s)
      Ueda Yoshimichi
    • Journal Title

      Canadian Journal of Mathematics

      Volume: 73 Issue: 2 Pages: 493-541

    • DOI

      10.4153/s0008414x20000048

    • NAID

      120007183218

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Free products in AQFT2019

    • Author(s)
      Longo Roberto、Tanimoto Yoh、Ueda Yoshimichi
    • Journal Title

      Annales de l'Institut Fourier

      Volume: 69 Issue: 3 Pages: 1229-1258

    • DOI

      10.5802/aif.3269

    • NAID

      120006716059

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] A free product pair rigidity result in von Neumann algebras2019

    • Author(s)
      Ueda Yoshimichi
    • Journal Title

      Journal of Noncommutative Geometry

      Volume: 13 Issue: 2 Pages: 587-607

    • DOI

      10.4171/jncg/332

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On Arveson's boundary theorem2019

    • Author(s)
      Kei Hasegawa and Yoshimichi Ueda
    • Journal Title

      Math. Proc. Royal Irish Acad.

      Volume: Vol.119A, No.1 Issue: 1 Pages: 1-5

    • DOI

      10.3318/pria.2019.119.01

    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Peer Reviewed
  • [Presentation] Spherical representations of C*-flows2022

    • Author(s)
      植田 好道
    • Organizer
      作用素環論の最近の進展, RIMS
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] Spherical representations for C*-flows2021

    • Author(s)
      Yoshimichi Ueda
    • Organizer
      C*-seminar, University of Oslo; Online.
    • Related Report
      2020 Annual Research Report
    • Invited
  • [Presentation] On Arveson's boundary theorem2020

    • Author(s)
      Yoshimichi Ueda
    • Organizer
      東大京大合同オンライン作用素環セミナー
    • Related Report
      2020 Annual Research Report
    • Invited
  • [Presentation] Matrix liberation process and orbital free entropy2020

    • Author(s)
      Yoshimichi Ueda
    • Organizer
      作用素環論研究者シンポジウム「作用素環論の最近の進展」Online
    • Related Report
      2020 Annual Research Report
    • Invited
  • [Presentation] On Arveson’s boundary theorem2019

    • Author(s)
      Yoshimichi Ueda
    • Organizer
      Interactions between Noncommutative Analysis and Quantum Information Theory
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Free independence, orbital free entropy and matrix liberation process2019

    • Author(s)
      Yoshimichi Ueda
    • Organizer
      Interactions between commutative and non-commutative probability
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] A new approach to free mutual information2019

    • Author(s)
      Yoshimichi Ueda
    • Organizer
      Non-commutative Probability and Related Fields
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] On Arveson’s boundary theorem2019

    • Author(s)
      植田 好道
    • Organizer
      作用素論・作用素環論研究集会
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] On Arveson's boundary theorem2019

    • Author(s)
      Yoshimichi Ueda
    • Organizer
      Seminario, Dipartimento di Matematica, Universita degli Studi di Roma Tor Vergata
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Remarks] 植田のホームページ(論文・プレプリント)

    • URL

      http://www.math.nagoya-u.ac.jp/~ueda/publ.html

    • Related Report
      2022 Annual Research Report 2021 Annual Research Report
  • [Remarks] 研究公表論文リスト

    • URL

      http://www.math.nagoya-u.ac.jp/~ueda/publ.html

    • Related Report
      2020 Annual Research Report
  • [Remarks] Homepage of Yoshimichi Ueda

    • URL

      http://www.math.nagoya-u.ac.jp/~ueda/index.html

    • Related Report
      2019 Annual Research Report
  • [Remarks] 植田好道のホームページ

    • URL

      http://www.math.nagoya-u.ac.jp/~ueda/index-j.html

    • Related Report
      2018 Annual Research Report

URL: 

Published: 2018-04-23   Modified: 2025-01-30  

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