Norm inequalities for the generalised commutator in Banach algebras

Abstract

. In this paper, by utilising the Riesz functional calculus in a Banach algebra B , we provide some norm inequalities for the generalized commutator f y ) z (cid:0) zf ( x ) where x; y; z 2 B and f is an analytic function for which the elements f ( y ) and f ( x ) exist. Some examples for the resolvent and exponential functions are also given.