International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 45, Pages 2377-2381
doi:10.1155/S0161171204402324

Stability of multipliers on Banach algebras

Takeshi Miura,1 Go Hirasawa,2 and Sin-Ei Takahasi1

1Department of Basic Technology, Yamagata University, Yonezawa 992-8510, Japan
2Department of Mathematics, Nippon Institute of Technology, Miyashiro, Saitama 345-8501, Japan

Received 2 February 2004

Copyright © 2004 Takeshi Miura 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

Suppose A is a Banach algebra without order. We show that an approximate multiplier T:A→A is an exact multiplier. We also consider an approximate multiplier T on a Banach algebra which need not be without order. If, in addition, T is approximately additive, then we prove the Hyers-Ulam-Rassias stability of T.