2012 Fiscal Year Final Research Report
Geometric topology of continuous function algebras
| Project/Area Number |
22540062
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | University of Tsukuba |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
KATO Hisao 筑波大学, 数理物質系, 教授 (70152733)
SAKAI Katsuro 筑波大学, 数理物質系, 准教授 (50036084)
KANETO Takeshi 筑波大学, 数理物質系, 講師 (70107340)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 連続関数環 / 力学系 / 群作用 |
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| Research Abstract |
Functional analytic study of dynamical system on compact metric was the central theme of the research based on the research grant. The focus is on theweighted composition operators on continuous function algebras. Associated with each dynamical system, an abelian group of unimodular weight for which the operators have eigenvalues was defined and it turned out the group carries both topological and measure theoretic aspects of the system. The result was generalized to group-action dynamics and an abelian group of 1-cocycle with similar property was defined and studied.
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