In this paper, we introduce the concept of pointwise compactness for a locally compact group $G,$ and among other results, we show that pointwise compactness of $G$ is a necessary condition for pointwise contractibility of $L^1(G)$ in a commutative case. Also, pointwise contractibility of measure algebras in a general case is studied. Finally, applying the results, we study the pointwise contractibility of Fourier and Fourier-Stieltjes algebras in a commutative case.
"Pointwise version of contractibility of Banach algebras of locally compact groups." Bull. Belg. Math. Soc. Simon Stevin 26 (1) 119 - 129, march 2019. https://doi.org/10.36045/bbms/1553047232