Research for the interplay between measurable dynamical systems and topological dynamical systems through the basic method of operator

• Project/Area Number: 24540195
• 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, 044, 教授 (10091620)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000); Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); 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: Hilbert space / Operator / Spectrum / C*-algebra / Dynamical system / positive functional / Banach algebra / operator / perturbation / Weyl's Theorem / n-paranormal / SVEP / Banach space / Fredholm Theory / Browder spectrum / symmetrizable operator / multioperator / Taylor spectrum

Outline of Final Research Achievements

On research for the interplay between measurable dynamical systems and topological dynamical systems through the bsasic method of operator theory, we have studied irreducible representations to Banach spaces (existence and etc.) and we showed that l^1（Σ) ia a Hermite algebra in the ideal structure problem of l^1（Σ). And we published a note with title "Note on the structure of non--commutative l^1-algebras associated with topological dynamical system".

Research Products

• [Journal Article] A note on cubically hyponormal weighted shifts (2014)
  • Author(s): C. Li, M. Cho and M.R. Lee
  • Journal Title: Bull. Korean Math. Soc. Volume: 51 Pages: 1031-1040
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Invariant subspace problem for ExB-operators (2014)
  • Author(s): M. Cho
  • Journal Title: unctional Analysis, Approximation and Computation Volume: 6:2 Pages: 61-64
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Reverses of the triangle inequalities in inner product spaces (2014)
  • Author(s): L. Zhang, T. Ohwada and M. Cho
  • Journal Title: Math. Inequalities and Applications Volume: 17 Issue: 2 Pages: 539-555
  • DOI: 10.7153/mia-17-41
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Transfinite ranges and the local spectrum (2013)
  • Author(s): M. Cho, R. Harte and V. Muller
  • Journal Title: J. Math. Anal. Appl. Volume: 398 Pages: 403-408
  • Peer Reviewed
• [Journal Article] On polynomially *-paranormal operators (2013)
  • Author(s): M. Cho, L. Zhang, A. Uchiyama and K. Tanahashi
  • Journal Title: Functional Analysis, Approximation and Computation Volume: 5:2 Pages: 11-16
  • Peer Reviewed
• [Journal Article] On *-n-paranormal operators (2013)
  • Author(s): M. Cho and S. Ota
  • Journal Title: Journal of Mathematics Research Volume: 5 Pages: 107-113
  • Peer Reviewed
• [Journal Article] Taylor exactness, SVEP and spectral mapping theorems (2013)
  • Author(s): M. Cho and R. Harte
  • Journal Title: J. Math. Forum Volume: 8 Pages: 1493-1501
  • Peer Reviewed
• [Journal Article] Invertible weighted shift operators which are m-isometries (2013)
  • Author(s): M. Cho, S. Ota and K. Tanahashi
  • Journal Title: Proc. Amer. Math. Soc. Volume: 141 Pages: 4241-4247
  • Peer Reviewed
• [Journal Article] On *-n-paranormal operators on Banach spaces (2013)
  • Author(s): M. Cho and K. Tanahashi
  • Journal Title: J. Math. Comput. Sci Volume: 4 Pages: 1-9
  • Peer Reviewed
• [Journal Article] Spectral commutativity of multioperators, (2012)
  • Author(s): M. Cho and V. Muller
  • Journal Title: Functional Analysis, Application and Computation Volume: 4:1 Pages: 21-25
  • Peer Reviewed
• [Journal Article] Spectral properties of m-isometric operators (2012)
  • Author(s): M. Cho, S. Ota, K. Tanahashi and A. Uchiyama
  • Journal Title: Functional Analysis, Application and Computation Volume: 4:2 Pages: 33-39
  • Peer Reviewed
• [Journal Article] Weyl's theorems and extensions of bounded operatprs (2012)
  • Author(s): P. Aiena, M. Cho, and L. Zhang
  • Journal Title: Tokyo J. Math. Volume: 35 Pages: 297-289
  • Peer Reviewed
• [Presentation] On m -isometric operators
  • Author(s): M. Cho
  • Organizer: Operators on Banach spaces
  • Place of Presentation: スペイン・Castro Urdiales
• [Presentation] Spectral properties of m-isometric operators
  • Author(s): 長 宗雄
  • Organizer: 太原理工大学理学部
  • Place of Presentation: 中国・太原理工大学
  • Invited
• [Presentation] An example of an m-isometry
  • Author(s): 長 宗雄、太田昇一、棚橋浩太朗
  • Organizer: 研究集会名「幾何学及び確率論的手法による作用素の構造解析の研究」
  • Place of Presentation: 京都大学数理解析研究所