Fuglede – Putnam Theorem For Class Operators

Abstract

        We say that the operators A,B on a Hilbert space satisfy Fuglede – Putnam theorem if AX=XB for some X implies that . In this paper , the hypotheses on A and B can be relaxed by using a Hilbert-Schmidt operator X : Let A belong to class  and let  be invertible operator belong to class  such that AX=XB for a Hilbert-Schmidt operator X ,then