Open Access

Spectrum of Class https://static-content.springer.com/image/art%3A10.1155%2F2007%2F27195/MediaObjects/13660_2006_Article_1688_IEq1_HTML.gif Operators

Journal of Inequalities and Applications20072007:027195

DOI: 10.1155/2007/27195

Received: 23 November 2006

Accepted: 16 May 2007

Published: 18 June 2007

Abstract

This paper discusses some spectral properties of class https://static-content.springer.com/image/art%3A10.1155%2F2007%2F27195/MediaObjects/13660_2006_Article_1688_IEq2_HTML.gif operators for https://static-content.springer.com/image/art%3A10.1155%2F2007%2F27195/MediaObjects/13660_2006_Article_1688_IEq3_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2007%2F27195/MediaObjects/13660_2006_Article_1688_IEq4_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2007%2F27195/MediaObjects/13660_2006_Article_1688_IEq5_HTML.gif , and https://static-content.springer.com/image/art%3A10.1155%2F2007%2F27195/MediaObjects/13660_2006_Article_1688_IEq6_HTML.gif . It is shown that if https://static-content.springer.com/image/art%3A10.1155%2F2007%2F27195/MediaObjects/13660_2006_Article_1688_IEq7_HTML.gif is a class https://static-content.springer.com/image/art%3A10.1155%2F2007%2F27195/MediaObjects/13660_2006_Article_1688_IEq8_HTML.gif operator, then the Riesz idempotent https://static-content.springer.com/image/art%3A10.1155%2F2007%2F27195/MediaObjects/13660_2006_Article_1688_IEq9_HTML.gif of https://static-content.springer.com/image/art%3A10.1155%2F2007%2F27195/MediaObjects/13660_2006_Article_1688_IEq10_HTML.gif with respect to each nonzero isolated point spectrum https://static-content.springer.com/image/art%3A10.1155%2F2007%2F27195/MediaObjects/13660_2006_Article_1688_IEq11_HTML.gif is selfadjoint and https://static-content.springer.com/image/art%3A10.1155%2F2007%2F27195/MediaObjects/13660_2006_Article_1688_IEq12_HTML.gif . Afterwards, we prove that every class https://static-content.springer.com/image/art%3A10.1155%2F2007%2F27195/MediaObjects/13660_2006_Article_1688_IEq13_HTML.gif operator has SVEP and property https://static-content.springer.com/image/art%3A10.1155%2F2007%2F27195/MediaObjects/13660_2006_Article_1688_IEq14_HTML.gif , and Weyl's theorem holds for https://static-content.springer.com/image/art%3A10.1155%2F2007%2F27195/MediaObjects/13660_2006_Article_1688_IEq15_HTML.gif when https://static-content.springer.com/image/art%3A10.1155%2F2007%2F27195/MediaObjects/13660_2006_Article_1688_IEq16_HTML.gif .

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Authors’ Affiliations

(1)
LMIB and Department of Mathematics, Beihang University
(2)
Dedicated to Professor Daoxing Xia on his 77th birthday with respect and affection

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Copyright

© J. Yuan and Z. Gao. 2007

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.