Title : ( Ultraweak continuity of σ-derivations on von Neumann algebras )
Authors: Madjid Mirzavaziri , Mohammad Sal Moslehian ,
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Abstract
Let σ be a surjective ultraweakly continuous ∗-linear mapping and d be a σ-derivation on a von Neumann algebra M. We show that there are a surjective ultraweakly continuous ∗-homomorphism : M → M and a - derivation D : M → M such that D is ultraweakly continuous if and only if so is d. We use this fact to show that the σ-derivation d is automatically ultraweakly continuous. We also prove the converse in the sense that if σ is a linear mapping and d is an ultraweakly continuous ∗-σ-derivation on M, then there is an ultraweakly continuous linear mapping : M → Msuch that d is a ∗--derivation.
Keywords
, Derivation · ∗, homomorphism · ∗, IWnneaekr σ(o, dpeerriavtaotrio) nto·pvoolnogNyeumann algebra · Uσlt, rdaewrievaaktitoonp·ology
@article{paperid:1010319,
author = {Madjid Mirzavaziri, and Sal Moslehian, Mohammad},
title = {Ultraweak continuity of σ-derivations on von Neumann algebras},
journal = {Mathematical Physics Analysis and Geometry},
year = {2009},
number = {12},
month = {April},
issn = {1385-0172},
pages = {109--115},
numpages = {6},
keywords = {Derivation · ∗-homomorphism · ∗-IWnneaekr σ(o-dpeerriavtaotrio) nto·pvoolnogNyeumann algebra · Uσlt-rdaewrievaaktitoonp·ology},
}
%0 Journal Article
%T Ultraweak continuity of σ-derivations on von Neumann algebras
%A Madjid Mirzavaziri,
%A Sal Moslehian, Mohammad
%J Mathematical Physics Analysis and Geometry
%@ 1385-0172
%D 2009
