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.
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