2013/07/03 by Mahmoud Filali, Filali, Mahmoud, Jorge Galindo +1
Mathematics · #22D15 #43A15 #43A46 #43A60 #54H11 #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN) #Group Theory (math.GR) #Operator Algebras (math.OA) #math.FA #math.GN #math.GR #math.OA #msc:22D15 #msc:43A15 #msc:43A46 #msc:43A60 #msc:54H11
paper · pdf · doi:10.48550/arxiv.1307.1000
arxiv created 2013/07/03 · arxiv updated 2013/07/04
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 L1(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^∞(G) in the quotient space L^∞(G)/CB(G), where CB(G) stands for the algebra of all continuous and bounded functions on G.