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Search: MSC category 47A05 ( General (adjoints, conjugates, products, inverses, domains, ranges, etc.) )

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1. CJM 2009 (vol 62 pp. 305)

Hua, He; Yunbai, Dong; Xianzhou, Guo
Approximation and Similarity Classification of Stably Finitely Strongly Irreducible Decomposable Operators
Let $\mathcal H$ be a complex separable Hilbert space and ${\mathcal L}({\mathcal H})$ denote the collection of bounded linear operators on ${\mathcal H}$. In this paper, we show that for any operator $A\in{\mathcal L}({\mathcal H})$, there exists a stably finitely (SI) decomposable operator $A_\epsilon$, such that $\|A-A_{\epsilon}\|<\epsilon$ and ${\mathcal{\mathcal A}'(A_{\epsilon})}/\operatorname{rad} {{\mathcal A}'(A_{\epsilon})}$ is commutative, where $\operatorname{rad}{{\mathcal A}'(A_{\epsilon})}$ is the Jacobson radical of ${{\mathcal A}'(A_{\epsilon})}$. Moreover, we give a similarity classification of the stably finitely decomposable operators that generalizes the result on similarity classification of Cowen-Douglas operators given by C. L. Jiang.

Keywords:$K_{0}$-group, strongly irreducible decomposition, Cowen—Douglas operators, commutant algebra, similarity classification
Categories:47A05, 47A55, 46H20

2. CJM 2005 (vol 57 pp. 61)

Binding, Paul; Strauss, Vladimir
On Operators with Spectral Square but without Resolvent Points
Decompositions of spectral type are obtained for closed Hilbert space operators with empty resolvent set, but whose square has closure which is spectral. Krein space situations are also discussed.

Keywords:unbounded operators, closed operators,, spectral resolution, indefinite metric
Categories:47A05, 47A15, 47B40, 47B50, 46C20

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