SOME VARIANTS OF WEBER'S THEOREM

Abstract

Weber's theorem says that if A : H → H is bounded and linear on a separable Hubert space, then any operator that is compact, commutes with A and lies in the weak closure of the range of the inner derivation induced by A must also be quasinilpotent. In this note we consider related problems for generalised inner derivations associated with operators A and B on H.