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On the essential norms of Toeplitz operators with symbols in C + H∞ acting on abstract Hardy spaces built upon translation-invariant Banach function spaces
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Resumo(s)
Let X be a translation-invariant Banach function space on the unit circle and let H[X] be the abstract Hardy space built upon X. We suppose the Riesz projection P is bounded on X and estimate the essential norms ‖T(a)‖B(H[X]),e of Toeplitz operators T(a)f:=P(af) with a∈C+H∞. We prove that in this case ‖a‖L∞≤‖T(a)‖B(H[X]),e≤min{2,‖P‖B(X)}‖a‖L∞, extending the results by the second author [27] for classical Hardy spaces Hp=H[Lp], 1<p<∞. In contrast to our previous works [27] and [16], we do not assume that X is reflexive or separable, which complicates the matters, but allows us to include the Hardy-Lorentz spaces Hp,q=H[Lp,q] with 1<p<∞ and q=1,∞ into consideration.
Descrição
Funding Information:
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:
© 2025 The Author(s)
Palavras-chave
Abstract Hardy space Essential norm Restricted dual compact approximation property Toeplitz operator Translation-invariant Banach function space General Mathematics