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Spectra of weighted composition operators on algebras of analytic functions on Banach spaces. (English) Zbl 1245.47014

Summary: Let \(E\) be a complex Banach space, with the unit ball \(B_{E}\). We study the spectrum of a bounded weighted composition operator \(uC_{\varphi }\) on \(H^{\infty }(B_E)\) determined by an analytic symbol \(\varphi \) with a fixed point in \(B_{E}\) such that \(\varphi (B_{E})\) is a relatively compact subset of \(E\), where \(u\) is an analytic function on \(B_{E}\).

MSC:

47B38 Linear operators on function spaces (general)
47B33 Linear composition operators
46E15 Banach spaces of continuous, differentiable or analytic functions
32A37 Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA))
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