LOCAL AUTOMORPHISMS OF OPERATOR ALGEBRAS

Abstract

A not necessarily continuous, linear or multiplicative function $\theta$ from an algebra $\mathcal A$ into itself is called a local automorphism if $\theta$ agrees with an automorphism of $\mathcal A$ at each point in $\mathcal A$. In this paper, we study the question when a local automorphism of a $C$*-algebra, or a W*-algebra, is an automorphism.