Eklund, T., Galindo, P., Lindström, M., Nieminen, I. (2017) Norm, essential norm and weak compactness of weighted composition operators between dual Banach spaces of analytic functions. Journal of Mathematical Analysis and Applications, 451 (1), 1-13. doi:10.1016/j.jmaa.2017.01.098

### Norm, essential norm and weak compactness of weighted composition operators between dual Banach spaces of analytic functions

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Author: Eklund, Ted1; Galindo, Pablo2; Lindström, Mikael1;
Organizations: 1Department of Mathematics, Åbo Akademi University, FI-20500 Åbo, Finland
2Departamento de Análisis Matemático, Universidad de Valencia, Spain
3Department of Mathematical Sciences, University of Oulu, Finland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 0.3 MB)
Language: English
Published: Elsevier, 2017
Publish Date: 2019-03-28
Description:

# Abstract

In this paper we estimate the norm and the essential norm of weighted composition operators from a large class of — non-necessarily reflexive — Banach spaces of analytic functions on the open unit disk into weighted type Banach spaces of analytic functions and Bloch type spaces. We also show the equivalence of compactness and weak compactness of weighted composition operators from these weighted type spaces into a class of Banach spaces of analytic functions, that includes a large family of conformally invariant spaces like BMOA and analytic Besov spaces.

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Series: Journal of mathematical analysis and applications
ISSN: 0022-247X
ISSN-E: 1096-0813
ISSN-L: 0022-247X
Volume: 451
Issue: 1
Pages: 1 - 13
DOI: 10.1016/j.jmaa.2017.01.098