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- W2022445947 abstract "In this paper we show that a Banach algebra A is amenable if and only if A has any one of the following properties: (i) whenever X is a Banach A-bimodule and Y is an A-submodule of X, then for each $f in {Y^ ast }$ such that $a cdot f = f cdot a,a in A$, there exists $tilde f in {X^ ast }$ which extends f and $a cdot tilde f = tilde f cdot a$ for all $a in A$; (ii) whenever X is a Banach A-bimodule, there exists a bounded projection P from ${X^ ast }$ onto {$f in {X^ ast };a cdot f = f cdot a$ for all $a in A$} such that $T cdot P = P cdot T$ for any $mathrm {weak}^*$ continuous bounded linear operator T from ${X^ ast }$ into ${X^ast }$ commuting with the action of A on ${X^ast }$. The class of ultraweakly amenable von Neumann algebras with separable predual can be similarly characterized." @default.
- W2022445947 created "2016-06-24" @default.
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- W2022445947 date "1978-02-01" @default.
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- W2022445947 title "Characterizations of amenable Banach algebras" @default.
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- W2022445947 doi "https://doi.org/10.1090/s0002-9939-1978-0492065-4" @default.
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