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• W2105408271 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 $mathsf{F}(A)$, the 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 Connes-amenability of $mathsf{F}(A)$. In particular we show that $mathsf{F}(A)$ is Connes-amenable if and only if $A$ admits a so-called $operatorname{WAP}$-virtual diagonal. We show that when $A=L^1(G)$, existence of a $operatorname{WAP}$-virtual diagonal is equivalent to the existence of a virtual diagonal in the usual sense. Our approach does not involve invariant means for $G$." @default.
• W2105408271 created "2016-06-24" @default.
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• W2105408271 date "2015-12-14" @default.
• W2105408271 modified "2023-10-14" @default.
• W2105408271 title "Extension of Derivations, and Connes- Amenability of the Enveloping Dual Banach Algebra" @default.
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• W2105408271 doi "https://doi.org/10.7146/math.scand.a-22870" @default.
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