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Non Commutative Arens Algebras and their Derivations | | S. Albeverio
; Sh. A. Ayupov
; K. K. Kudaybergenov
; | | Date: |
6 Mar 2007 | | Subject: | Functional Analysis; Operator Algebras | | Abstract: | Given a von Neumann algebra $M$ with a faithful normal semi-finite trace $ au,$ we consider the non commutative Arens algebra $L^{omega}(M, au)=igcaplimits_{pgeq1}L^{p}(M, au)$ and the related algebras $L^{omega}_2(M, au)=igcaplimits_{pgeq2}L^{p}(M, au)$ and $M+L^{omega}_2(M, au)$ 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 $M+L^{omega}_2(M, au)$ is inner and all derivations of the algebras $L^{omega}(M, au)$ and $L^{omega}_2(M, au)$ are spatial and implemented by elements of $M+L^{omega}_2(M, au).$ | | Source: | arXiv, math/0703170 | | Services: | Forum | Review | PDF | Favorites | |
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