Journal of Inequalities and Applications (Dec 2007)
Spectrum of Compact Weighted Composition Operators on the Weighted Hardy Space in the Unit Ball
Abstract
Let BN be the unit ball in the N-dimensional complex space, for È, a holomorphic function in BN, and Õ, a holomorphic map from BN into itself, the weighted composition operator on the weighted Hardy space H2(β,BN) is given by (CÈ,Õ)f=È(z)f(Õ(z)), where f∈H2(β,BN). This paper discusses the spectrum of CÈ,Õ when it is compact on a certain class of weighted Hardy spaces and when the composition map Õ has only one fixed point inside the unit ball.