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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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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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 / Hilbert space / linear operator / paranprmal operator / normaloid / m-isometry / Bishop property / Banach space / Polaloid operator / 力系 / normal operator / Polaroid operator / elementary operator / numerical range / normal opreator / Bishop's property / composition operator / operator equation / spectrum |
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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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Report
(6 results)
Research Products
(60 results)
