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RANGE –KERNEL ORTHOGONALITY OF ELEMENTARY CHORDAL TRANSFORM | ||
| Journal of Al-Nahrain University - Science | ||
| Article 1, Volume 10, Issue 2, 2007, Pages 149-153 | ||
| Authors | ||
| Buthainah Abdul; Hasan Ahmed; Sudad Musa Rasheed | ||
| Abstract | ||
| Let B(H)denoted the * C algebra of all bounded linear operators on a separable Hilbert space H . For A,BB(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) by 2 1 / 2 A,B 1 / 2 2 * A,B g (X) ( A I) (X)(B I) for all X B(H) .In this paper ,the Range –kernel orthogonality of this transform was studied concerning to main rants , the Range – kernel orthogonality of the restrictions of A B g , to Hilbert –Schmidt class and the Range–Kernel orthogonality of restrictions A B f , and A B g , to Schatten p-class. | ||
| Keywords | ||
| Normal derivation; schatten p; class; unitarily invariant norm; orthogonality; elementary operator; chordal transform | ||
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