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Search: All articles in the CMB digital archive with keyword von Neumann algebra

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1. CMB 2016 (vol 59 pp. 326)

Jiang, Chunlan; Shi, Rui
On the Uniqueness of Jordan Canonical Form Decompositions of Operators by $K$-theoretical Data
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
Categories:47A15, 47C15, 47A65

2. CMB 2016 (vol 59 pp. 320)

Ino, Shoji
Perturbations of Von Neumann Subalgebras with Finite Index
In this paper, we study uniform perturbations of von Neumann subalgebras of a von Neumann algebra. Let $M$ and $N$ be von Neumann subalgebras of a von Neumann algebra with finite probabilistic index in the sense of Pimsner-Popa. If $M$ and $N$ are sufficiently close, then $M$ and $N$ are unitarily equivalent. The implementing unitary can be chosen as being close to the identity.

Keywords:von Neumann algebras, perturbations
Categories:46L10, 46L37

3. CMB 2006 (vol 49 pp. 371)

Floricel, Remus
Inner $E_0$-Semigroups on Infinite Factors
This paper is concerned with the structure of inner $E_0$-semigroups. We show that any inner $E_0$-semigroup acting on an infinite factor $M$ is completely determined by a continuous tensor product system of Hilbert spaces in $M$ and that the product system associated with an inner $E_0$-semigroup is a complete cocycle conjugacy invariant.

Keywords:von Neumann algebras, semigroups of endomorphisms, product systems, cocycle conjugacy
Categories:46L40, 46L55

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