Quasitriangular + small compact = strongly irreducible
Author:
You Qing Ji
Journal:
Trans. Amer. Math. Soc. 351 (1999), 46574673
MSC (1991):
Primary 47A10, 47A55, 47A58
Published electronically:
July 20, 1999
MathSciNet review:
1603910
Fulltext PDF Free Access
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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:
http://dx.doi.org/10.1090/S0002994799023077
PII:
S 00029947(99)023077
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
