Journal of Operator Theory

Volume 90, Issue 1, Summer 2023 pp. 171-189.

Compact weighted composition operators on spaces of holomorphic functions on Banach spaces

Authors: Jose Bonet (1), David Jornet (2), Daniel Santacreu (3), and Pablo Sevilla-Peris (4)
Author institution: (1) Instituto Universitario de Matematica Pura y Aplicada IUMPA, Universitat Politecnica de Valencia, Valencia, E-46022, Spain
(2) Instituto Universitario de Matematica Pura y Aplicada IUMPA, Universitat Politecnica de Valencia, Valencia, E-46022, Spain
(3) Instituto Universitario de Matematica Pura y Aplicada IUMPA, Universitat Politecnica de Valencia, Valencia, E-46022, Spain
Instituto Universitario de Matematica Pura y Aplicada IUMPA, Universitat Politecnica de Valencia, Valencia, E-46022, Spain

Summary: Given an infinite dimensional Banach space $X$ and its open unit ball $B$ , we study when the weighted composition operator $C_{\psi,\varphi}$ is compact in the space of all bounded analytic functions $H^\infty(B)$ , and when it is bounded, reflexive, Montel and (weakly) compact in the space of analytic functions of bounded type $H_\mathrm b(B)$ . The study is given in terms of properties of the weight $\psi$ and the symbol $\varphi$ .

DOI: http://dx.doi.org/10.7900/jot.2021nov03.2365
Keywords: Compact operator, weighted composition operator, holomorphic function on a Banach space.

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