Abstract view
Approximation and Similarity Classification of Stably Finitely Strongly Irreducible Decomposable Operators


Published:20091204
Printed: Apr 2010
He Hua
Dong Yunbai
Guo Xianzhou
Abstract
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 $\AA_{\epsilon}\<\epsilon$ 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 CowenDouglas operators given by C. L. Jiang.
MSC Classifications: 
47A05, 47A55, 46H20 show english descriptions
General (adjoints, conjugates, products, inverses, domains, ranges, etc.) Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15] Structure, classification of topological algebras
47A05  General (adjoints, conjugates, products, inverses, domains, ranges, etc.) 47A55  Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15] 46H20  Structure, classification of topological algebras
