Open Access

Spectrum of Compact Weighted Composition Operators on the Weighted Hardy Space in the Unit Ball

Journal of Inequalities and Applications20072007:061313

DOI: 10.1155/2007/61313

Received: 28 February 2007

Accepted: 19 October 2007

Published: 31 December 2007

Abstract

Let be the unit ball in the -dimensional complex space, for , a holomorphic function in , and , a holomorphic map from into itself, the weighted composition operator on the weighted Hardy space is given by , where . This paper discusses the spectrum of when it is compact on a certain class of weighted Hardy spaces and when the composition map has only one fixed point inside the unit ball.

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Authors’ Affiliations

(1)
Department of Mathematics, Tianjin University

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Copyright

© Z.-H. Zhou and C. Yuan. 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.