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On the essential norms of Toeplitz operators on abstract Hardy spaces built upon Banach function spaces
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Orientador(es)
Resumo(s)
Let X be a Banach function space over the unit circle such that the Riesz projection P is bounded on X and let H[X] be the abstract Hardy space built upon X. We show that the essential norm of the Toeplitz operator T(a):H[X]→H[X] coincides with ‖a‖L∞ for every a∈C+H∞ if and only if the essential norm of the backward shift operator T(e-1):H[X]→H[X] is equal to one, where e-1(z)=z-1. This result extends an observation by Böttcher, Krupnik, and Silbermann for the case of classical Hardy spaces.
Descrição
Funding Information:
Open access funding provided by FCT|FCCN (b-on). This work is funded by national funds through the FCT - Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 (https://doi.org/10.54499/UIDB/00297/2020) and UIDP/ 00297/2020 (https://doi.org/10.54499/UIDP/00297/2020) (Center for Mathematics and Applications).
Publisher Copyright:
© The Author(s) 2024.
Palavras-chave
Abstract Hardy space Banach function space Essential norm Toeplitz operator General Mathematics