Development around various type entropy as well as operator algebraic basic research on measurable dynamical system and topological dynamical system

• Project/Area Number: 15K04910
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kanagawa University
• Principal Investigator: Cho Muneo 神奈川大学, 理学部, 教授 (10091620)
• Project Period (FY): 2015-04-01 – 2020-03-31
• Project Status: Completed (Fiscal Year 2019)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: Entropy / Hilbert space / Operator Theory / dynamical system / Banach space / spectrum / entropy / operator algebra / operator / conjugation / numerical range / isometry / C^*-algebra / symmetry / Cの*乗-algebra / ∞-isometric

Outline of Final Research Achievements

Conjugation is defined in a Hilbert space. That is, it is defined by the inner product. By this definition, we have many papers of conjugations. We defined the conjugation in a Banach space. By this, we studied characterization of the spectrum and the numerical range of an operator concerning with a conjugation. From now on, conjugation on a Banach space we will be studied.

Academic Significance and Societal Importance of the Research Achievements

これまで conjugation はヒルベルト空間の時のみに定義されていたのであるが、これをより一般のバナッハ空間上に定義することができたので、今後これに関連した研究が進められると考える。

Research Products

• [Journal Article] On operators T commuting with CTC where C is a conjugation (2020)
  • Author(s): M. Cho, E. Ko, J.E. Lee
  • Journal Title: Bull. Korean Math. Soc. Volume: 57 Pages: 69-79
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] On the approximate point spectra of m-complex symmetric operators, [m,C]-symmetric operators and others (2019)
  • Author(s): M. Cho, J.E. Lee, B. Nacevska Nastovska, T. Saito
  • Journal Title: Functional Analysis, Application Computation Volume: 11(1) Pages: 11-20
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Fuglede-Putnam Theorem and quasisimilarity of class p-wA(s,t) operators (2019)
  • Author(s): M. Cho, T. Prasad, M.H.M. Rashid, K. Tanahashi, A. Uchiyama
  • Journal Title: Operators and Matrices Volume: 13 Issue: 1 Pages: 293-299
  • DOI: 10.7153/oam-2019-13-19
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] CLASS p-wA(s, t) OPERATORS AND RANGE KERNEL RTHOGONALITY (2019)
  • Author(s): M. Cho, T. Prasad, M.H.M. Rashid, K. Tanahashi, A. Uchiyama
  • Journal Title: Scientiae Mathematicae Japonicae Volume: 82 Issue: 1 Pages: 45-55
  • DOI: 10.32219/isms.82.1_45
  • NAID: 130007681539
  • ISSN: 1346-0447
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Complex symmetric operators and isotopic vectors on Banach spaces (2019)
  • Author(s): M. Cho, Injo Hur, J.E. Lee
  • Journal Title: J. Math. Anal. Appl. Volume: 479 Issue: 1 Pages: 752-764
  • DOI: 10.1016/j.jmaa.2019.06.049
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] (A,m)-symmetric commuting tuples of operators on a Hilbert space (2019)
  • Author(s): M. Cho, O.A.M.Sid Ahmd
  • Journal Title: Math. Ineq. Appl. Volume: 22 Issue: 3 Pages: 931-947
  • DOI: 10.7153/mia-2019-22-63
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Skew m-complex symmetric operators (2019)
  • Author(s): M. Cho, E. Ko, J.E. Lee
  • Journal Title: Filomat Volume: 33 Issue: 10 Pages: 2975-2983
  • DOI: 10.2298/fil1910975c
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Spectral properties of square hyponormal operators (2019)
  • Author(s): M. Cho, D. Mosic, B. Nacevska Nastovska, T. Saito
  • Journal Title: Filomat Volume: 33-15 Issue: 15 Pages: 4845-4854
  • DOI: 10.2298/fil1915845c
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] On (m,C)-isometric commuting tuples of operators on a Hilbert space (2018)
  • Author(s): O.A.M. Sid Ahmd, M. Cho and J.E. Lee
  • Journal Title: Results in Mathematics Volume: 73 Issue: 2 Pages: 5101-5131
  • DOI: 10.1007/s00025-018-0810-0
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Complex isosymmetric operators (2018)
  • Author(s): M. Cho, J.E. Lee, T. Prasad and K. Tanahashi
  • Journal Title: Adv. Oper. Theory Volume: 3 Issue: 3 Pages: 620-631
  • DOI: 10.15352/aot.1712-1267
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Three-operator problem in Banach spaces (2018)
  • Author(s): M. Cho, J. Castillo and M. Gonzalez
  • Journal Title: Extracta Math. Volume: 33 Issue: 2 Pages: 149-165
  • DOI: 10.17398/2605-5686.33.2.149
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] On [m, C]- symmetric operators (2018)
  • Author(s): M. Cho, J.E. Lee, K. Tanahashi and J. Tomiyama
  • Journal Title: Kyungpook Math. J. Volume: 58 Pages: 637-650
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Spectral properties of n-normal operators (2018)
  • Author(s): M. Cho and Biljana Nacevska
  • Journal Title: Filomat Volume: 32 Issue: 14 Pages: 5063-5069
  • DOI: 10.2298/fil1814063c
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Remarks on n-normal operators (2018)
  • Author(s): M. Cho, J.E. Lee, K. Tanahashi and A. Uchiyama
  • Journal Title: Filomat Volume: 32 Issue: 15 Pages: 5441-5451
  • DOI: 10.2298/fil1815441c
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Weyl's theorem and Putnam's Inequality for class p-wA(s,t) operators (2018)
  • Author(s): M. Cho, M.H.M. Rashid, T. Prasad, K. Tanahashi and A. Uchiyama
  • Journal Title: Acta Sci. Math. (Szeged) Volume: 84 Issue: 3-4 Pages: 573-589
  • DOI: 10.14232/actasm-017-020-y
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] On ∞-complex symmetric operators (2018)
  • Author(s): M. Cho, E. Ko and J.E. Lee
  • Journal Title: Glasgow Math. J. Volume: 60 Issue: 1 Pages: 35-50
  • DOI: 10.1017/s0017089516000550
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] On [m,C]-complex symmetric operators (2017)
  • Author(s): M. Cho, J.E. Lee and H. Motoyoshi
  • Journal Title: Filomat Volume: 31 Issue: 7 Pages: 2073-2080
  • DOI: 10.2298/fil1707073c
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Properties of m-complex symmetric operators (2017)
  • Author(s): M. Cho, E. Ko and J.E. Lee
  • Journal Title: Stud. Univ. Babes-Bolyai Math. Volume: 62 Issue: 2 Pages: 233-248
  • DOI: 10.24193/subbmath.2017.2.09
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] (∞, C)-isometric operators (2017)
  • Author(s): M. Cho, E. Ko, Ji E. Lee
  • Journal Title: Operators and Matrices Volume: 11 Issue: 3 Pages: 793-806
  • DOI: 10.7153/oam-11-56
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] On skew [m,C]-symmetric operators (2017)
  • Author(s): M. Cho, Biljana Nacevska and J. Tomiyama
  • Journal Title: Adv. Oper. Theory Volume: 2 Pages: 468-474
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] The pertubation classes for closed operators (2017)
  • Author(s): P. Aiena, M. Cho, M. Gonzalez
  • Journal Title: Filomat Volume: 31:3 Issue: 3 Pages: 2073-2080
  • DOI: 10.2298/fil1703621a
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] On symmetric and skew symmetric operators (2017)
  • Author(s): C. Benhida, M. Cho, E. Ko and J.E. Lee
  • Journal Title: Filomat Volume: 31 Issue: 1 Pages: 2073-2080
  • DOI: 10.2298/fil1801293b
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Elementary properties of ∞-isometric operators on a Hilbert space (2016)
  • Author(s): M. Cho, C. Gu, Woo Y. Lee
  • Journal Title: Linear Algebra Appl. Volume: 511 Pages: 378-402
  • DOI: 10.1016/j.laa.2016.09.023
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] On m-complex symmetric operators (2016)
  • Author(s): M. Cho, E. Ko, Ji E. Lee
  • Journal Title: Mediter. J. Math. Volume: 13 Pages: 2025-2038
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] On (m,C)-isometric (2016)
  • Author(s): M. Cho, E. Ko and J.E. Lee
  • Journal Title: Complex Anal. Oper. Theory. Volume: 4 Issue: 8 Pages: 1-16
  • DOI: 10.1007/s11785-016-0549-0
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] On m-complex symmetric operators II (2016)
  • Author(s): M. Cho, E. Ko, Ji E. Lee
  • Journal Title: Mediter. J. Math. Volume: 13 Issue: 5 Pages: 3255-3264
  • DOI: 10.1007/s00009-016-0683-y
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Spectrum of class p-wA(s,t) operators (2016)
  • Author(s): M. Cho, M. Rashid, K. Tanahashi, A. Uchiyama
  • Journal Title: Acta Sci. Math. (Szeged) Volume: 82 Issue: 3-4 Pages: 641-649
  • DOI: 10.14232/actasm-015-275-0
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] operatorsOn m-complex symmetric operators (2015)
  • Author(s): M. Cho, E. Ko and J.E. Lee
  • Journal Title: Mediterr. J. Math. Volume: 20 Pages: 1-14
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Presentation] Numerical ranges of Banach space operators (2019)
  • Author(s): M. Cho
  • Organizer: The fifteenth workshop on numerical ranges and numerical radii
  • Int'l Joint Research
• [Presentation] On n-normal operators and others (2019)
  • Author(s): M. Cho
  • Organizer: KOTAC2019
  • Int'l Joint Research
• [Presentation] Numerical ranges of a Banach space operator (2019)
  • Author(s): M. Cho
  • Organizer: KOTAC2019
  • Int'l Joint Research
• [Presentation] Approximate point spectra of m-complex symmetric operators and others (2019)
  • Author(s): M. Cho
  • Organizer: 順序を用いた作用素の構造研究と関連する話題
• [Presentation] Remarks on conjugation and antilinear operators and their numerical range (2019)
  • Author(s): M. Cho
  • Organizer: 順序を用いた作用素の構造研究と関連する話題
• [Presentation] クラス p-wA(s,t) 作用素上の spectral continuity (2019)
  • Author(s): K. Tanahashi
  • Organizer: 順序を用いた作用素の構造研究と関連する話題
• [Presentation] Linear operators on a Banach space (2018)
  • Author(s): M. Cho
  • Organizer: KOTAC 2018
• [Presentation] 線形作用素の conjugation に係る話題 (2018)
  • Author(s): M. Cho
  • Organizer: 第57回実函数論・函数解析学合同シンポジウム
• [Presentation] Linear operators and Conjugations on a Banach space (2018)
  • Author(s): M. Cho and H. Motoyoshi
  • Organizer: 作用素平均を利用した作用素の構造解析の研究と関連する話題
• [Presentation] On n-normal operators (2018)
  • Author(s): M. Cho
  • Organizer: 作用素平均を利用した作用素の構造解析の研究と関連する話題
• [Presentation] On class p-wA(s,t) operators (2018)
  • Author(s): K. Tanahashi and M. Cho
  • Organizer: 作用素平均を利用した作用素の構造解析の研究と関連する話題
• [Presentation] m-isometric and m-symmetric operators (2017)
  • Author(s): M. Cho
  • Organizer: 関東作用素論研究会
  • Place of Presentation: 東京理科大学
  • Year and Date: 2017-01-21
• [Presentation] Furuta's inequality and p-wA(s,t) operators (2017)
  • Author(s): M. Cho
  • Organizer: International Workshop of Operator Theory and Applications 2017
  • Int'l Joint Research
• [Presentation] On conjugation and linear operator II (2017)
  • Author(s): M. Cho
  • Organizer: BANACH空間に基づく技法による作用素論の最近の研究と関連する話題
• [Presentation] 線形作用素と Conjugation (2017)
  • Author(s): M. Cho
  • Organizer: 作用素論・作用素環論研究集会
• [Presentation] 種々の不等式について (2017)
  • Author(s): M. Cho
  • Organizer: 上越地区高等学校数学教育研究会
• [Presentation] Furuta inequality and p-wA(s,t) operators (2016)
  • Author(s): 棚橋浩太郎
  • Organizer: 作用素論に基づく量子情報理論の幾何学的構造に関する研究と関連する話題
  • Place of Presentation: 京都大学数理解析所
  • Year and Date: 2016-11-11
• [Presentation] On conjugation and linear operator (2016)
  • Author(s): M. Cho
  • Organizer: 作用素論に基づく量子情報理論の幾何学的構造に関する研究と関連する話題
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2016-11-09
• [Presentation] On ∞-complex symmetric operators (2016)
  • Author(s): M. Cho
  • Organizer: SWOT 2016
  • Place of Presentation: クラコフ
  • Year and Date: 2016-07-06
  • Int'l Joint Research
• [Presentation] On m -isometric operators (2015)
  • Author(s): M. Cho
  • Organizer: 順序と幾何による作用素の構造研究と関連する話題
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2015-11-09
• [Presentation] Spectral properties of m-complex symmetric operators (2015)
  • Author(s): J.E. Lee
  • Organizer: The 14th KOTAC International Conference 2015
  • Place of Presentation: 韓国・Daejeon
  • Year and Date: 2015-06-18
  • Int'l Joint Research
• [Book] 関数解析入門 線形作用素のスペクトル (2018)
  • Author(s): 荷見守助、長 宗雄、瀬戸道生
  • Total Pages: 248
  • Publisher: 内田老鶴圃