Generalized Weighted Composition Operators on Vector-Valued Weighted Bergman Space

In this research article the necessary and sufficient conditions for the norm of composition operator C_Φ on 𝒜_α^2(H) to be one are obtained. Moreover, C_Φ is unitary on 𝒜_α^2(H) if and only if it is co-isometry. The necessary and sufficient condition for Hermitian and normal composition operators on 𝒜_α^2(H) are also explored. Also, the characterization for boundedness of generalized weighted composition operator is obtained under some condition on Φ .