Numerical ranges of weighted composition operators. (English) Zbl 07087223
Summary: In this paper, first we consider the numerical range of \(C_{\psi, \varphi}\), when \(\varphi(z) = r z\) with \(| r | \leq 1\). Then we study the numerical range of \(C_{\psi, \varphi}\), where \({\varphi}\) is an elliptic automorphism. Next, the exact value of the norm of some weighted composition operators are obtained in order to investigate their numerical radiuses. Finally, we compute the numerical ranges of all hermitian weighted composition operators.
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