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

2019 Fiscal Year Final Research Report

• 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
• Keywords: Entropy / Hilbert space / Operator Theory / dynamical system / Banach space

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.

Free Research Field

関数解析学

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。