ADJOINTS OF WEIGHTED COMPOSITIONOPERATORS ON HILBERT SPACES OFANALYTIC FUNCTIONS IN THE UNITBALL AND ITS APPLICATIONS

摘要

This paper presents a general formula for the adjoint of a weighted composition operatoravailable for all admissible cp and φ in any Hilbert spaces of analytic functions with repro-ducing kernels. Based on this, some improved explicit expressions for the adjoint of C_(φ,φ)induced by specific φand φare obtained, and the characterization forto be self-adjointon the weighted Bergman space is also given.