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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Bishop's property ($\beta $) and essential spectra
of quasisimilar operators


Authors: Lin Chen and Yan Zikun
Journal: Proc. Amer. Math. Soc. 128 (2000), 485-493
MSC (1991): Primary 47B40, 47A10
Published electronically: May 19, 1999
MathSciNet review: 1625717
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Abstract | References | Similar Articles | Additional Information

Abstract: We analyze the notion of Bishop's property ($\beta $) to obtain some new concepts. We describe some conditions in terms of these concepts for an operator to have its essential spectrum (spectrum) contained in the essential spectrum (spectrum) of every operator quasisimilar to it. A subfamily of such operators is proved to be dense in $L(\mathbf{H})$.


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Additional Information

Lin Chen
Affiliation: Department of Mathematics, Fujian Normal University, Fuzhou, 350007, The People’s Republic of China
Email: xhyan@fjtu.edu.cn

Yan Zikun
Affiliation: Department of Mathematics, Fujian Normal University, Fuzhou, 350007, The People’s Republic of China

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05047-9
PII: S 0002-9939(99)05047-9
Keywords: Quasisimilarity, essential spectra, subdecomposability
Received by editor(s): March 27, 1998
Published electronically: May 19, 1999
Additional Notes: This research was supported by the National Natural Science Foundation of China
Communicated by: David R. Larson
Article copyright: © Copyright 1999 American Mathematical Society