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On the Uniqueness of Jordan Canonical Form Decompositions of Operators by $K$-theoretical Data

Published:2016-03-03
Printed: Jun 2016
• Chunlan Jiang,
Department of Mathematics, , Hebei Normal University, , Hebei, 050024, China
• Rui Shi,
School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China
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Abstract

In this paper, we develop a generalized Jordan canonical form theorem for a certain class of operators in $\mathcal {L}(\mathcal {H})$. A complete criterion for similarity for this class of operators in terms of $K$-theory for Banach algebras is given.
 Keywords: strongly irreducible operator, similarity invariant, reduction theory of von Neumann algebras, $K$-theory
 MSC Classifications: 47A15 - Invariant subspaces [See also 47A46] 47C15 - Operators in $C^*$- or von Neumann algebras 47A65 - Structure theory

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