Extreme non-Arens regularity of the group algebra
Functional Analysis
2013-07-04 v1 General Topology
Group Theory
Operator Algebras
Abstract
Following Granirer, a Banach algebra A is extremely non-Arens regular when the quotient space A*/WAP(A) contains a closed linear subspace which has A* as a continuous linear image. We prove that the group algebra L^1(G) of any infinite locally compact group is always extremely non-Arens regular. When G is not discrete, this result is deduced from the much stronger property that, in fact, there is a linear isometric copy of L^\infty(G) in the quotient space L^\infty(G)/CB(G), where CB(G) stands for the algebra of all continuous and bounded functions on G.
Keywords
Cite
@article{arxiv.1307.1000,
title = {Extreme non-Arens regularity of the group algebra},
author = {Mahmoud Filali and Jorge Galindo},
journal= {arXiv preprint arXiv:1307.1000},
year = {2013}
}