Commutators in Banach algebras

Abstract

In a recent paper ( 6 ) the present author has shown that, for an element a of a Banach algebra A , the condition for all x ∈ A and some constant α is equivalent to [ x , a ]∈Rad a for all x ∈ A ; it turns out that α may be replaced by |α|σ It is the purpose of the present note to investigate a related condition