Pointwise version of contractibility of Banach algebras of locally compact groups. (English) Zbl 1416.43004

Soroushmehr, M.

Bull. Belg. Math. Soc. - Simon Stevin 26, No. 1, 119-129 (2019).

In a previous paper [Semigroup Forum 93, No. 2, 211–224 (2016; Zbl 1360.43002)] the author introduced the notion of pointwise contractible Banach algebra and, among other results, showed that if the group algebra \(\ell^1(G)\) of a discrete group \(G\) is pointwise contractible, then \(G\) is periodic.
Here the author continues the study of pointwise contractibility for the group algebras associated to a locally compact group. He introduces the notion of pointwise compact group and shows that it is a necessary condition for pointwise contractibility of \(L^1(G)\) when \(G\) is abelian. He also studies pointwise contractibility of measure algebras in the general case, and applies the results to the Fourier algebra \(A(G)\) and the Fourier-Stieltjes algebra \(B(G)\) for commutative groups \(G\) satisfying some conditions.

Reviewer: Manuel González (Santander)

MSC:

43A20	\(L^1\)-algebras on groups, semigroups, etc.
22B10	Structure of group algebras of LCA groups

Keywords:

group algebras; pointwise contractibility

Citations:

Zbl 1360.43002