On A-Commuting Operators

Abstract

Two bounded linear operators A and B on a complex Hilbert space are said to ,1.- commute for ,lEe provided that: AB = ABA. In this paper we look for some properties satisfied by the operators A and B so that ,1.= 1. It is shown among other results that if one of the operators raised to some power is normal and 0 does not belong to the interior of the numerical range of the other operator then: A = 1 AMS 200 Mathematics Subject Classification 47B47 47 A30, 47B20