Quotient Arens regularity of $L^1(G)$

Subject Areas : History and biography

A.  Zivari-Kazempour ¹ (Department of Mathematics, University of Ayatollah Borujerdi, Borujerd, Iran)

Received: 2015-12-09 Accepted : 2016-02-28 Published : 2015-12-01

Keywords: Arens product, Quotient Arens regular, Introverted subspace, Weakly almost periodic,

Abstract :

Let $\mathcal{A}$ be a Banach algebra with BAI and $E$ be an introverted subspace of $\mathcal{A}^\prime$.In this paper we study the quotient Arens regularity of $\mathcal{A}$ with respect to $E$ and prove that the group algebra $L^1(G)$ for a locally compact group $G$, is quotient Arens regular with respect to certain introverted subspace $E$ of $L^\infty(G)$.Some related result are given as well.

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