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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