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

2013/05/24 by Rui Shi, Shi, Rui
Mathematics · #47A65 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #Primary 47A15 #Secondary 47C15

paper · pdf · doi:10.48550/arxiv.1305.5651

openalex publication_date 2013/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the structure of operators in a type I_n von Neumann algebra \mathscrA. Inspired by the Jordan canonical form theorem, our main motivation is to figure out the relation between the structure of an operator A in \mathscrA and the property that a bounded maximal abelian set of idempotents contained in the relative commutant \A\^′ ∩\mathscrA is unique up to similarity. Furthermore, we classify this class of operators with the property by K-theory for Banach algebras. Some views and techniques are from von Neumann's reduction theory.

Citations

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

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