Indexed by: Journal Article
Date of Publication: 2014-01-01
Journal: Houston Journal of Mathematics
Included Journals: Scopus、SCIE
Volume: 40
Issue: 4
Page Number: 1183-1224
ISSN: 0362-1588
Key Words: Strongly irreducible operator; similarity invariant; reduction theory of von Neumann algebras; K-theory
Abstract: In this paper, we study the structures of operators in a type I-n von Neumann algebra A. As an analogue of the Jordan canonical form theorem, for an operator A in A, we prove that if {A}' boolean AND A contains a bounded maximal Boolean algebra of idempotents, then the bounded maximal Boolean algebras of idempotents in the relative commutant {A}' boolean AND A are the same up to similarity. Meanwhile we characterize the structures for operators in A whose relative commutants contain bounded maximal Boolean algebras of idempotents. We also classify this class of operators by K-theory for Banach algebras. We use techniques of von Neumann's reduction theory in our proofs.