Approximation and Similarity Classification of Stably Finitely Strongly Irreducible Decomposable Operators

Hua, He ; Yunbai, Dong ; Xianzhou, Guo

Canadian journal of mathematics, Tome 62 (2010) no. 2, pp. 305-319

Résumé

Let $\mathcal{H}$ be a complex separable Hilbert space and $\mathcal{L}\left( \mathcal{H} \right)$ denote the collection of bounded linear operators on $\mathcal{H}$ . In this paper, we show that for any operator $A\,\in \,\mathcal{L}\left( \mathcal{H} \right)$ , there exists a stably finitely $\left( \text{SI} \right)$ decomposable operator ${{A}_{\epsilon }}$ , such that $\left\| A-{{A}_{\epsilon }} \right\|\,<\,\epsilon$ and ${{\mathcal{A}}^{\prime }}\left( {{A}_{\epsilon }} \right)/\text{rad}\,{{\mathcal{A}}^{\prime }}\left( {{A}_{\epsilon }} \right)$ is commutative, where rad ${{\mathcal{A}}^{\prime }}\left( {{A}_{\epsilon }} \right)$ is the Jacobson radical of ${{\mathcal{A}}^{\prime }}\left( {{A}_{\epsilon }} \right)$ . 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.

Détail

DOI : 10.4153/CJM-2010-018-5

Mots-clés : 47A05, 47A55, 46H20, K 0-group, strongly irreducible decomposition, Cowen–Douglas operators, commutant algebra, similarity classification