Quasi-multipliers on group algebras related to a locally compact group

Authors

  • Mohammad Javad Mehdipour Department of Mathematics, Shiraz University of Technology, Shiraz 71555-313, Iran
  • Gholam Reza Moghimi Department of Mathematics, Payame Noor University(PNU), P.OBox, 19395-4697 Tehran, Iran

Keywords:

Locally compact group, quasi-multiplier, measure algebra, weakly compact operator

Abstract

In this paper, we first characterize quasi-multipliers of $(M({\cal G})_0^*)^*$ and show that the Banach algebra of all quasi-multipliers of $(M({\cal G})_0^*)^*$ is isometrically isomorphic to $(M({\cal G})_0^*)^*$. We also establish that quasi-multipliers of $(M({\cal G})_0^*)^*$ are separately continuous. Then, we investigate the existence of weakly compact quasi-multipliers of $(M({\cal G})_0^*)^*$. Finally, we prove that the Banach algebra of quasi-multipliers of $(M({\cal G})_0^*)^*$  is commutative if and only if ${\cal G}$ is abelian and discrete.

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Published

2021-08-30

Issue

Vol. 16

Section

Vol. 16, No. 1, (2022)

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