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

By Trieu Le. 2012

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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 − 〈 z , w 〉 ) − γ for γ > 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.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/b38197d8e3fb9f3caac9b3647ac6f01b4592f8e3