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Non-commutative Arens algebras and their derivations by S. Albeverio; Sh.A. Ayupov; K.K. Kudaybergenov is a Mathematics article available to read on EtoBox.

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Given a von Neumann algebra M with a faithful normal semi-finite trace τ , we consider the non-commutative Arens algebra L ω (M, τ ) = p 1 L p (M, τ ) and the related algebras L ω 2 (M, τ ) = p 2 L p (M, τ ) and M +L ω 2 (M, τ ) which are proved to be complete metrizable locally convex \*-algebras. The main purpose of the present paper is to prove that any derivation of the algebra M + L ω 2 (M, τ ) is inner and all derivations of the algebras L ω (M, τ ) and L ω 2 (M, τ ) are spatial and implemented by elements of M + L ω 2 (M, τ ). In particular we obtain that if the trace τ is finite then any derivation on the noncommutative Arens algebra L ω (M, τ ) is inner.

Who reads Non-commutative Arens algebras and their derivations?

Author

S. Albeverio; Sh.A. Ayupov; K.K. Kudaybergenov

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-1236)

Published

2007

Language

EN

Field

Mathematics (Physical Sciences)