## Amenability and weak amenability of second conjugate Banach algebras.(English)Zbl 0851.46035

Proc. Am. Math. Soc. 124, No. 5, 1489-1497 (1996); addendum ibid. 148, No. 10, 4573-4575 (2020).
Summary: 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.

### MSC:

 46H20 Structure, classification of topological algebras 43A20 $$L^1$$-algebras on groups, semigroups, etc.

### Keywords:

weak amenability; locally compact group
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### References:

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