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Essential spectra of quasisimilar -quasihyponormal operators

Journal of Inequalities and Applications20062006:72641

https://doi.org/10.1155/JIA/2006/72641

©  A.-H. Kim and I. H. Kim 2006

Received: 1 July 2005

Accepted: 20 September 2005

Published: 20 April 2006

Abstract

It is shown that if is an upper-triangular operator matrix acting on the Hilbert space and if denotes the essential spectrum, then the passage from to is accomplished by removing certain open subsets of from the former. Using this result we establish that quasisimilar -quasihyponormal operators have equal spectra and essential spectra.

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Authors’ Affiliations

(1)
Department of Mathematics, Changwon National University
(2)
Department of Mathematics, Seoul National University

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Copyright

© A.-H. Kim and I. H. Kim 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.