On the norm of an inner derivation of a C*-algebra

Abstract

Let A be a C*-algebra with centre Z. If a ∈ A, the bounded linear mapping x → + ax – xa (x ∈ A) is called the inner derivation of A induced by a, and we denote it by D(a, A). A simple application of the triangle inequality shows thatwhere d (a; Z) denotes the distance from a to Z in the normed space A.