Choi, Yemon and Samei, Ebrahim and Stokke, Ross (2015) Extension of derivations, and Connesamenability of the enveloping dual Banach algebra. Mathematica Scandinavica, 117 (2). pp. 258303. ISSN 00255521

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Abstract
If $D:A \to X$ is a derivation from a Banach algebra to a contractive, Banach $A$bimodule, then one can equip $X^{**}$ with an $A^{**}$bimodule structure, such that the second transpose $D^{**}: A^{**} \to X^{**}$ is again a derivation. We prove an analogous extension result, where $A^{**}$ is replaced by $\F(A)$, the \emph{enveloping dual Banach algebra} of $A$, and $X^{**}$ by an appropriate kind of universal, enveloping, normal dual bimodule of $X$. Using this, we obtain some new characterizations of Connesamenability of $\F(A)$. In particular we show that $\F(A)$ is Connesamenable if and only if $A$ admits a socalled WAPvirtual diagonal. We show that when $A=L^1(G)$, existence of a WAPvirtual diagonal is equivalent to the existence of a virtual diagonal in the usual sense. Our approach does not involve invariant means for $G$.
Item Type:  Journal Article 

Journal or Publication Title:  Mathematica Scandinavica 
Uncontrolled Keywords:  /dk/atira/pure/subjectarea/asjc/2600 
Subjects:  
Departments:  Faculty of Science and Technology > Mathematics and Statistics 
ID Code:  73427 
Deposited By:  ep_importer_pure 
Deposited On:  13 Apr 2015 15:50 
Refereed?:  Yes 
Published?:  Published 
Last Modified:  20 Feb 2020 02:12 
URI:  https://eprints.lancs.ac.uk/id/eprint/73427 
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