2016 Fiscal Year Final Research Report
| Project/Area Number |
26400102
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Hokkaido University |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2017-03-31
|
| Keywords | 力学系 / 接合積 / バナッハスター環 / Cスター環 / 既約表現 / エルゴード変換 / エルゴード拡張 |
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| Outline of Final Research Achievements |
We show how to construct irreducible representations of the Banach *-algebra associated with a dynamical system in general, which consists of two major
procedures including what we call ergodic extension. An ergodic extension of a ergodic transformation on a (quasi-invariant) non-atomic probability measure space is an extension of the given one to an ergodic transformation of the system obtained by tensoring with a Type I factor. It is not clear this is at all possible. We were unable to prove this in general but show this is possible by two examples in the finite type I case, Bernoulli shifts and irrational rotations, whose proof depends on detailed property of these transformations.
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| Free Research Field |
作用素環
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