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Self-adjoint, unitary, and normal weighted composition operators in several variables (1207.5980v1)
Published 25 Jul 2012 in math.FA
Abstract: We study weighted composition operators on Hilbert spaces of analytic functions on the unit ball with kernels of the form $(1-<z,w>){-\gamma}$ for $\gamma>0$. We find necessary and sufficient conditions for the adjoint of a weighted composition operator to be a weighted composition operator or the inverse of a weighted composition operator. We then obtain characterizations of self-adjoint and unitary weighted composition operators. Normality of these operators is also investigated.