On the unitary equivalence of close \(C^ *\)-algebras
Let A be a \(C^*\)-algebra which is either commutative or separable unital with a continuous trace. Suppose D and D' are subalgebras of a common \(C^*\)-algebra and D is an extension of A by the compacts. It is shown that if the Hausdorff distance between their unit balls is sufficiently small, then D and D' are unitarily equivalent.
scientific article; zbMATH DE number 3969406