Another Generalization of Anderson's Theorem

Abstract

In this paper, we prove that if A and B are normal operators on a Hubert space H , then, for every operator 5 satisfying ASB = , \\AXB-X+ S > IMII-'PH-'IISII for all operators X e B(H), and that if A and B are contractions, then, for every operator satisfying ASB = and A'SB* = , \\AXB - X + S > \\S for all operators X e B(H), where B(H) denotes the set of all bounded linear operators on H.