Abstract and Applied Analysis
Volume 2011 (2011), Article ID 235273, 30 pages
http://dx.doi.org/10.1155/2011/235273
Research Article

Quasimultipliers on 𝐹 -Algebras

Marjan Adib,1 Abdolhamid Riazi,2 and Liaqat Ali Khan3

1Department of Mathematics, Payamenoor University-Aligodarz Branch, Aligodarz, Iran
2Department of Mathematics and Computer Science, Amirkabir University of Technology, P.O. Box 15914, Tehran, Iran
3Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received 7 June 2010; Revised 24 October 2010; Accepted 25 January 2011

Academic Editor: Wolfgang Ruess

Copyright © 2011 Marjan Adib et al. 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 investigate the extent to which the study of quasimultipliers can be made beyond Banach algebras. We will focus mainly on the class of 𝐹 -algebras, in particular on complete 𝑘 -normed algebras, 0 < 𝑘 ≤ 1 , not necessarily locally convex. We include a few counterexamples to demonstrate that some of our results do not carry over to general 𝐹 -algebras. The bilinearity and joint continuity of quasimultipliers on an 𝐹 -algebra 𝐴 are obtained under the assumption of strong factorability. Further, we establish several properties of the strict and quasistrict topologies on the algebra 𝑄 𝑀 ( 𝐴 ) of quasimultipliers of a complete 𝑘 -normed algebra 𝐴 having a minimal ultra-approximate identity.