2011 Fiscal Year Final Research Report
Research in the noncommutative dynamical systems through the method of functional analysis together with the research in the interplay between topological dynamical systems and operator theory
| Project/Area Number |
20540192
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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 |
Basic analysis
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| Research Institution | Kanagawa University |
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Principal Investigator |
CHO Muneo 神奈川大学, 工学部, 教授 (10091620)
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| Co-Investigator(Renkei-kenkyūsha) |
TOMIYAMA Jun 東京都立大学, 名誉教授
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| Project Period (FY) |
2008 – 2011
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| Keywords | 量子力学 / 力学系 / ヒルベルト空間 / 線形作用素 / スペクトル |
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| Research Abstract |
Operator algebras corresponding to topological dynamical systems have been studied as C-clossed products. On the other hand, there are Banach-algebra clossed products. These differences are the existence of non-self sdjoint closed ideal. One of the main results is the following : Every closed ideal of l^1 is self adjoint if and only if its dynamical system is free. Commutants of algebras are commutative maximal Banach-algebras and the intersection of closed ideals is non empty. We proved it for Banach-algebras and showed the existence projections to the maximal abelian subalgebras. As a more closing Are semi-hyponormal operators convexoid? This is a open problem for 20 years. About this problem, we could show that if, for the unilateral shift U, put S=T^2, then S is convexoid. It is published from the journal Linear and Multilinear Algebra with title"A remark on numerical range of semi-hyponormal operators". Next we studied Polaroid operators on a Banach space. We showed that if Polaroid operators have single value extension property, then Weyl's Theorem holds for these operators. Also we showed that if an operator T is quasi-similar with Bishop property and Polaroid, then T is Polaroid. These results are published from Journal of Mathematical Analysis and Applications.
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