Completely Continuous Linear Maps on Semigroup Algebra
Bulletin of the Malaysian Mathematical Society, Tome 36 (2013) no. 1
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For a locally compact group $G$, $L^1(G)$ is its group algebra and $L^\infty(G)$ is the dual of $L^1(G)$. Crombez and Govaerts introduced the notion of a uniformly measurable function in $L^\infty(G)$ and proved that such a function induces a completely continuous operator. The aim of this paper is to go further and generalize the above results to foundation semigroup algebras. We study completely continuous linear maps on semigroup algebras which commute with translations.
Classification :
Primary: 43A22; Secondary: 43A60
Ali Ghaffari. Completely Continuous Linear Maps on Semigroup Algebra. Bulletin of the Malaysian Mathematical Society, Tome 36 (2013) no. 1. http://geodesic.mathdoc.fr/item/BMMS_2013_36_1_a13/
@article{BMMS_2013_36_1_a13,
author = {Ali Ghaffari},
title = {Completely {Continuous} {Linear} {Maps} on {Semigroup} {Algebra}},
journal = {Bulletin of the Malaysian Mathematical Society},
year = {2013},
volume = {36},
number = {1},
url = {http://geodesic.mathdoc.fr/item/BMMS_2013_36_1_a13/}
}