A similarity invariant of a class of n-normal operators in terms of K-theory

2012/11/27 by Chunlan Jiang, Rui Shi, Jiang, Chunlan +1 · 1 citation
Mathematics · #47A15 #47A65 #47C15 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1211.6243

openalex publication_date 2012/11/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove an analogue of the Jordan canonical form theorem for a class of n-normal operators on complex separable Hilbert spaces in terms of von Neumann's reduction theory. This is a continuation of our study of bounded linear operators, the commutants of which contain bounded maximal abelian set of idempotents. Furthermore, we give a complete similarity invariant for this class of operators by K-theory for Banach algebras.

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• A reduction theory for operators in type \rmI_n von Neumann algebras

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