The Essential Norms of Toeplitz Operators with Symbols in C+H∞ on Weighted Hardy Spaces are Independent of the Weights

Karlovych, Oleksiy; Shargorodsky, Eugene

http://hdl.handle.net/10362/184909

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Autores

Karlovych, Oleksiy

Shargorodsky, Eugene

Resumo(s)

Let 1<p<∞, let Hp be the Hardy space on the unit circle, and let Hp(w) be the Hardy space with a Muckenhoupt weight w∈Ap on the unit circle. In 1988, Böttcher, Krupnik and Silbermann proved that the essential norm of the Toeplitz operator T(a) with a∈C on the weighted Hardy space H2(ϱ) with a power weight ϱ∈A2 is equal to ‖a‖L∞. This implies that the essential norm of T(a) on H2(ϱ) does not depend on ϱ. We extend this result and show that if a∈C+H∞, then, for 1<p<∞, the essential norms of the Toeplitz operator T(a) on Hp and on Hp(w) are the same for all w∈Ap. In particular, if w∈A2, then the essential norm of the Toeplitz operator T(a) with a∈C+H∞ on the weighted Hardy space H2(w) is equal to ‖a‖L∞.

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: © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.