| Abstrakt: |
Let L(H) denote the algebra of operators on a complex infinite dimensional Hilbert space H and let J denote a two-sided ideal in L(H). Given A,B ∈ L(H), define the generalized derivation δA,B as an operator on L(H) by δA,B(X) = AX - XB. We say that the pair of operators (A,B) has the Fuglede-Putnam property (PF)J if AT = TB and T ∈ J implies A*T = TB*. In this paper, we give operators A,B for which the pair (A,B) has the property (PF)J. We establish the orthogonality of the range and the kernel of a generalized derivation δA,B for non-normal operators A,B ∈ L(H). We also obtain new results concerning the intersection of the closure of the range and the kernel of δA,B. [ABSTRACT FROM AUTHOR] |
