Perturbation theory for groups and lattices
This paper contains a generalization of a theorem of Voiculescu which shows that, under separability assumptions, certain perturbed (by compacts) \(C^*\)-algebras of operators are unitarily equivalent. It is shown that this conclusion may fail in the inseparable case. The author gives reasons for seeking a generalization to certain inseparable \(C^*\)-algebras and, among other results, obtains such a generalization. This is applied to solve a problem relating to the perturbation theory of unitary group representations and to a problem of commutative subspace lattices, which extends a theorem of Anderson on compact perturbations of nests.
perturbation theory of unitary group representations
scientific article; zbMATH DE number 3863919
scientific article