Abstract
Let H denote a complex Hubert space, L(H) the algebra of all bounded linear operators on H and C₁(H), the trace class operators. We study the pairs of operators A, B εL(H) with the property that AT= TB and T εC₁ (H) implies B*T = TA*. The main result is that this property is equivalent to the self-adjointness of the ultraweak closure of the range of a generalised derivation.
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