Operator Inequalities and Spectral Analysis of Non-normal operators
| Project/Area Number |
20540198
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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 | Yamagata University |
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Principal Investigator |
UCHIYAMA Atsushi Yamagata University, 理学部, 准教授 (00353227)
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| Project Period (FY) |
2008 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 作用素論 / 非正規作用素 / SVEP / normaloid / ワイルの定理 / フグレデ・パットナムの定理 / クラスA作用素 / 正規作用素 / 作用素不等式 / ハイポノーマル / スペクトラム / リース射影 / ノルム不等式 / (p, k)-quasihyponormal / quasi-class (A, k) / Riesz idempoten / Weyl' s theorem |
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| Research Abstract |
My research is to characterize the classes of operators which are defined by operator inequalities or operator norm inequalities. The following two results are main results in this period :
(1) We show that for a (p,k)-pquasihyponormal operator T and a non-zero isolated point λ of its spectrum, λis an eigenvalue of T and the Riesz idempotent E is self-adjoint whose image is equal to the kernel of T-λ. As a corollary, we obtain that every (p,k)-quasihyponormal operator satisfies Weyl's theorem,
(2) We define three properties (I), (I'), (II) of (approximate point) spectrum of operators and show that every operator with at least one of these properties has Bishop's property (β) and (SVEP), moreover, we show that every paranormal operator has Bishop's property (β) and (SVEP). By using Birkoff-James orthogonality, we extend property (II) and show that every operator with this property has Bishop's property (β) and (SVEP). As a corollary, we obtain that every hereditarily normaloid operator has Bishop's property (β) and (SVEP).
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Report
(4 results)
Research Products
(16 results)
