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arXiv · 1207.5980

Self-adjoint, unitary, and normal weighted composition operators in several variables

Trieu Le
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Abstract

We study weighted composition operators on Hilbert spaces of analytic functions on the unit ball with kernels of the form $(1- )^{-\gamma}$ 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.

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Trieu Le. 2012-07-25. Self-adjoint, unitary, and normal weighted composition operators in several variables. https://doi.org/10.1016/j.jmaa.2012.05.065

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