RANGE –KERNEL ORTHOGONALITY OF ELEMENTARY CHORDAL TRANSFORM

Abstract

Let B(H)denoted the  * C algebra of all bounded linear operators on a separable Hilbertspace H . For A,BB(H) , the elementary operator : ( ) ( ) , B H B H A B   is defined byX  AXB X A B    , .We defined the elementary Chordal transform A B g , as an operator on B(H) by2 1 / 2A,B1 / 22*A,B g (X) ( A I) (X)(B I)      for all X B(H) .In this paper ,the Range –kernel orthogonalityof this transform was studied concerning to main rants , the Range – kernel orthogonality of therestrictions of A B g , to Hilbert –Schmidt class and the Range–Kernel orthogonality of restrictionsA B f , and A B g , to Schatten p-class.