Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 61313, 8 pages
doi:10.1155/2007/61313
Research Article

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

Ze-Hua Zhou and Cheng Yuan

Department of Mathematics, Tianjin University, Tianjin 300072, China

Received 28 February 2007; Accepted 19 October 2007

Academic Editor: András Rontó

Copyright © 2007 Ze-Hua Zhou and Cheng Yuan. 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.

Abstract

Let BN be the unit ball in the N-dimensional complex space, for ψ, a holomorphic function in BN, and ϕ, a holomorphic map from BN into itself, the weighted composition operator on the weighted Hardy space H2(β,BN) is given by (Cψ,ϕ)f=ψ(z)f(ϕ(z)), where f∈H2(β,BN). This paper discusses the spectrum of Cψ,ϕ when it is compact on a certain class of weighted Hardy spaces and when the composition map ϕ has only one fixed point inside the unit ball.