Range Kernel Orthogonality of Generalized Derivations
A. Bachi · International Journal of Open Problems in Computer Science and Mathematics · 2012
We say that the operators A;B on Hilbert space satisfy the Fuglede-Putnam theorem if AX = XB for some X implies A X = XB . We show that if A is k quasihyponormal and B is an injective p hyponormal operator, then A;B satisfy the Fuglede-Putnam theorem. As a consequence of this result, we obtain the range of the generalized derivation induced by the above classes of operators is orthogonal to its kernel.