Quasitriangular + small compact = strongly irreducible
Authors:
You Qing Ji
Affiliation:
Department of Mathematics, Jilin University, Changchun 130023, P.R. China
Abstract:
Let be a bounded linear operator acting on a separable infinite dimensional Hilbert space. Let be a positive number. In this article, we prove that the perturbation of by a compact operator with can be strongly irreducible if is a quasitriangular operator with the spectrum connected. The Main Theorem of this article nearly answers the question below posed by D. A. Herrero.
Suppose that is a bounded linear operator acting on a separable infinite dimensional Hilbert space with connected. Let be given. Is there a compact operator with such that is strongly irreducible?