Structures of some weighted composition operators on the space of square integrable functions with respect to a positive measure
Let T be the unit circle,(mu) be a Borel probability measure on T and (phi) be a bounded Lebesgue measurable function on T. in this paper we consider the weighted composition operator W(phi) on L^2(T,mu) defined by W(phi)f:=(phi)*(f(circle)(tau)), f in L^2(T), where (tau) is the map (tau)(z)=z^2, z in T. We will study the von Neumann-Wold decomposition of W(phi) when W(phi) is an isometry and (mu)<< m,where m is the normalized Lebesgue measure on T.
Advisor:Jhishen Tsay; Mark C. Ho; Ngai-Ching Wong; Pei Yuan Wu
School:National Sun Yat-Sen University
School Location:China - Taiwan
Source Type:Master's Thesis
Keywords:weighted composition operator shift isometry
Date of Publication:06/12/2002