Open Access

A Hilbert-Type Linear Operator with the Norm and Its Applications

Journal of Inequalities and Applications20092009:494257

DOI: 10.1155/2009/494257

Received: 9 February 2009

Accepted: 9 March 2009

Published: 31 March 2009

Abstract

A Hilbert-type linear operator is defined. As for applications, a more precise operator inequality with the norm and its equivalent forms are deduced. Moreover, three equivalent reverses from them are given as well. The constant factors in these inequalities are proved to be the best possible.

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Authors’ Affiliations

(1)
Department of Mathematics, Guangdong Institute of Education

Copyright

© Wuyi Zhong. 2009

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.