Bulletin of Australian Mathematical Society, ( ISI ), No (79), Year (2009-4) , Pages (249-257)

Title : ( A Kadison-Sakai type theorem )

Authors: Madjid Mirzavaziri , Mohammad Sal Moslehian ,

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Suppose that $\\\\sigma:\\\\calm\\\\to\\\\calm$ is an ultraweakly continuous surjective $*$-linear mapping and $d:\\\\calm\\\\to\\\\calm$ is an ultraweakly continuous $*$-$\\\\sigma$-derivation such that $d(I)$ is a central element of $\\\\calm$. We provide a Kadison--Sakai type theorem by proving that $\\\\calh$ can be decomposed into ${\\\\calk}\\\\oplus{\\\\call}$ and $d$ can be factored as the form $\\\\delta\\\\oplus 2Z\\\\tau$, where $\\\\delta:{\\\\calm}\\\\to\\\\calm$ is an inner $*$-$\\\\sigma_{\\\\calk}$-derivation, $Z$ is a central element, $2\\\\tau=2\\\\sigma_{\\\\call}$ is a $*$-homomorphism, and $\\\\sigma_{\\\\calk}$ and $\\\\sigma_{\\\\call}$ stand for compressions of $\\\\sigma$ to $\\\\calk$ and $\\\\call$, respectively.


, Derivation, $*$-homomorphism, $*$-$\\\\sigma$-derivation, inner $\\\\sigma$-derivation, $*$-$(\\\\sigma, \\\\tau)$-derivation, Kadison--Sakai theorem, ultraweak (operator) topology
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author = {Mirzavaziri, Madjid and Sal Moslehian, Mohammad},
title = {A Kadison-Sakai type theorem},
journal = {Bulletin of Australian Mathematical Society},
year = {2009},
number = {79},
month = {April},
issn = {0004-9727},
pages = {249--257},
numpages = {8},
keywords = {Derivation; $*$-homomorphism; $*$-$\\\\sigma$-derivation; inner $\\\\sigma$-derivation; $*$-$(\\\\sigma;\\\\tau)$-derivation; Kadison--Sakai theorem; ultraweak (operator) topology},


%0 Journal Article
%T A Kadison-Sakai type theorem
%A Mirzavaziri, Madjid
%A Sal Moslehian, Mohammad
%J Bulletin of Australian Mathematical Society
%@ 0004-9727
%D 2009