Proceedings of the Edinburgh Mathematical Society (Series 2)

Table of Contents - February 1997 - Volume 40, Issue 01  

Research Article

Essentially defined derivations on semisimple Banach algebras

A. R. Villenaa1

a1 Departamento de Análisis Matemático, Universidad de Granada, 18071 Granada, Spain, E-mail address: avillena@goliat.ugr.es

Abstract

We prove that every partially defined derivation on a semisimple complex Banach algebra whose domain is a (non necessarily closed) essential ideal is closable. In particular, we show that every derivation defined on any nonzero ideal of a prime C*-algebra is continuous.

(Received May 31 1995)