On dual of group algebras under a locally convex topology

Document Type : Original Paper

Authors

1 Department of Mathematics, Semnan University, Semnan, Iran

2 Department of Mathematics, Velayat University, Iranshahr, Iran

Abstract

For a locally compact group $G$, $L^1(G)$ is its group algebra and $L^\infty(G)$ is the dual of $L^1(G)$. We consider

on $L^\infty(G)$ the $\tau$-topology, i.e. the weak topology under all right multipliers induced

by measures in $L^1(G)$. For such an arbitrary $G$ the $\tau$-topology is not weaker than the

weak$^*$-topology and not stronger than the norm topology on $L^\infty(G)$. Among the other results we mention that except

for discrete $G$ the $\tau$-topology is always different from the norm-topology. The properties of $\tau$ are then studied further and we pay attention to the $\tau$-almost periodic elements of $L^\infty(G)$.

Keywords

Main Subjects


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