Compactness and weak compactness of weighted composition operators on BMOA

Laitila, Jussi; Lindström, Mikael; Norrbo, David

doi:10.1090/proc/16203

Compactness and weak compactness of weighted composition operators on BMOA
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by Jussi Laitila, Mikael Lindström and David Norrbo;

Proc. Amer. Math. Soc. 151 (2023), 1195-1207

DOI: https://doi.org/10.1090/proc/16203

Published electronically: November 4, 2022

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Abstract:

We show that a weighted composition operator ${W_{\psi ,\varphi }}$ is compact on BMOA precisely when it is unconditionally converging. As a direct consequence to this result we deduce that all weakly compact or completely continuous weighted composition operators on BMOA are compact. The proof of this result is based on a new simplified function-theoretic characterization of the compactness of weighted composition operators on BMOA.

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