Class

Abstract

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