Amenability and weak amenability of second conjugate Banach algebras

Ghahramani, F.; Loy, R.; Willis, G.

doi:10.1090/S0002-9939-96-03177-2

Amenability and weak amenability of second conjugate Banach algebras
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by F. Ghahramani, R. J. Loy and G. A. Willis PDF

Proc. Amer. Math. Soc. 124 (1996), 1489-1497 Request permission

Addendum: Proc. Amer. Math. Soc. 148 (2020), 4573-4575.

Abstract:

For a Banach algebra $\mathfrak {A}$, amenability of $\mathfrak {A}^{**}$ necessitates amenability of $\mathfrak {A}$, and similarly for weak amenability provided $\mathfrak {A}$ is a left ideal in $\mathfrak {A}^{**}$. For $\mathfrak {G}$ a locally compact group, indeed more generally, $L^1(\mathfrak {G})^{**}$ is amenable if and only if $\mathfrak {G}$ is finite. If $L^1(\mathfrak {G})^{**}$ is weakly amenable, then $M(\mathfrak {G})$ is weakly amenable.

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