Biquasitriangular operators have strongly irreducible perturbations.

Jiang, Chun Lan and Power, Stephen C. and Wang, Zong Yao (2000) Biquasitriangular operators have strongly irreducible perturbations. The Quarterly Journal of Mathematics, 51 (3). pp. 353-369. ISSN 0033-5606

Abstract

We prove that if T is a biquasitriangular operator on a Hilbert space H with connected spectrum then T may be approximated by a strongly irreducible operator S with S _ T compact and small.