LINEAR DERIVATIONS ON BANACH ALGEBRAS

Abstract

It is shown that for an almost derivation on a Banach algebra B; there exists a unique C-linear derivation D: B-> B near the almost derivation. Moreover, we prove that for an almost *-derivation on a C*-algebra B; there exists a unique C-linear *-derivation D : B-> B near the almost *-derivation, and that for an almost ¤-derivation on a JB*-algebra B; there exists a unique C-linear *-derivation D : B-> B near the almost  *-derivation.