Pointwise version of contractibility of Banach algebras of locally compact groups (Q2418795)

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. \par 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.