On The Range of Generalized Jordan *-derivation

Abstract

Let H be an infinite dimensional separable complex Hilbert space and let B(H) be the algebra of bounded liners operators in H.Let A,BB(H), the generalized Jordan *-derivations JA,B :B(H) B(H) is defined by:JA,B(X) =XA BX*,XB(H)In this paper we study some properties of the range of generalized Jordan *-derivations, which is represented by RA,B, and defined by: RA,B={XABX*: XB(H)}.