摘要
In this note, all the Hilbert spaces mentioned are separable. Let H, and H2 be Hilbert spaces, B(H2, H1) the set of all bounded linear transformations from H2 to H2. Let A and B belong to B(H1) and B(H2) respectively. Define an operator δBA on B(H2, H1) by δAB(x) = AX— XB, X∈ B(H2, H1), we call it a generalized derivation. R(δAB) denotes the range of δAB.