Quasitriangular + small compact

= strongly irreducible

Author:
You Qing Ji

Journal:
Trans. Amer. Math. Soc. **351** (1999), 4657-4673

MSC (1991):
Primary 47A10, 47A55, 47A58

DOI:
https://doi.org/10.1090/S0002-9947-99-02307-7

Published electronically:
July 20, 1999

MathSciNet review:
1603910

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?

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Additional Information

**You Qing Ji**

Affiliation:
Department of Mathematics, Jilin University, Changchun 130023, P.R. China

DOI:
https://doi.org/10.1090/S0002-9947-99-02307-7

Keywords:
Weyl spectrum,
index,
strongly irreducible,
quasitriangular

Received by editor(s):
May 23, 1997

Published electronically:
July 20, 1999

Additional Notes:
This work is supported by MCSEC

Article copyright:
© Copyright 1999
American Mathematical Society