Approximation and Similarity Classification of Stably Finitely Strongly Irreducible Decomposable Operators
| Autor: | He Hua, Dong Yunbai, Guo Xianzhou |
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| Rok vydání: | 2010 |
| Předmět: | |
| Zdroj: | Canadian Journal of Mathematics. 62:305-319 |
| ISSN: | 1496-4279 0008-414X |
| DOI: | 10.4153/cjm-2010-018-5 |
| Popis: | Let 𝓗 be a complex separable Hilbert space and ℒ(𝓗) denote the collection of bounded linear operators on 𝓗. In this paper, we show that for any operator A ∈ ℒ(𝓗), there exists a stably finitely (SI) decomposable operator A∈, such that ‖A−A∈‖ 𝓗 ∈ andA′(A∈)/ rad A′(A∈) is commutative, where rad A′(A∈) is the Jacobson radical of A′(A∈). 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. |
| Databáze: | OpenAIRE |
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