Generalized D-symmetric Operators II

摘要

Let H be a separable, infinite-dimensional, complex Hilbert space and let A, B ∈ L(H), where L(H) is the algebra of all bounded linear operators on H. Let δ_(AB): L(H) → L(H) denote the generalized derivation δ_(AB)(X) = AX ? XB. This note will initiate a study on the class of pairs (A, B) such that R(δAB) = R(δ_(A*B*)).