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Generalized Weighted Composition Operators on Vector-Valued Weighted Bergman Space (2308.05230v1)
Published 9 Aug 2023 in math.FA
Abstract: In this research article the necessary and sufficient conditions for the norm of composition operator $C_{\Phi}$ on $\mathcal{A}{\alpha}2(H)$ to be one are obtained. Moreover, $C{\Phi}$ is unitary on $\mathcal{A}{\alpha}2(H)$ if and only if it is co-isometry. The necessary and sufficient condition for Hermitian and normal composition operators on $\mathcal{A}{\alpha}2(H)$ are also explored. Also, the characterization for boundeness of generalized weighted composition operator is obtained under some condition on $\Phi.$