Weak amenability of group algebras. (English) Zbl 0757.43002

This paper provides a proof that if \(G\) is a locally compact group then the algebra \(L^ 1(G)\) is weakly amenable, that is any derivation from \(L^ 1(G)\) to \(L^ \infty(G)\) is inner.


43A20 \(L^1\)-algebras on groups, semigroups, etc.
43A07 Means on groups, semigroups, etc.; amenable groups
46M20 Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.)
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