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

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.