Central Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra ( JLTA )2252-0201040420151201Quotient Arens regularity of $L^1(G)$275281520428ENA.Zivari-KazempourDepartment of Mathematics, University of Ayatollah Borujerdi, Borujerd, IranJournal Article20151209Let $mathcal{A}$ 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.http://jlta.iauctb.ac.ir/article_520428_4afeac134e032a7734d87bb8535bcc8d.pdf