Abstract and Applied Analysis
Volume 2011 (2011), Article ID 680952, 6 pages
http://dx.doi.org/10.1155/2011/680952
Research Article

Arens Regularity of Certain Class of Banach Algebras

Abbas Sahleh and Abbas Zivari-Kazempour

Department of Mathematics, University of Guilan, P.O. Box 1914, Rasht, Iran

Received 6 February 2011; Accepted 2 May 2011

Academic Editor: Marcia Federson

Copyright © 2011 Abbas Sahleh and Abbas Zivari-Kazempour. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study Arens regularity of the left and right module actions of 𝐴 on 𝐴 ( 𝑛 ) , where 𝐴 ( 𝑛 ) is the nth dual space of a Banach algebra 𝐴 , and then investigate (quotient) Arens regularity of 𝑈 = 𝐴 ⊕ 𝐴 ( 𝑛 ) as a module extension of Banach algebras.