**Financial support through the following projects:**

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UID/MAT/00297/2019

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PEst-OE/MAT/UI0297/2014

PEst-OE/MAT/UI0297/2011

On the essential norms of Toeplitz operators

by Eugene Shargorodsky, King's College London, United Kingdom

Data: 26/09/2018

Hora: 14h00

Local: Sala 1.4 - Edifício VII, FCT-UNL

Resumo

It is well known that the essential norm of a Toeplitz operator on the Hardy space $H^p(\mathbb{T})$, $1 < p < \infty$, is greater than or equal to the supremum norm of its symbol. In 1988, A. B\"ottcher, N. Krupnik, and B. Silbermann posed a question on whether or not the equality holds in the case of continuous symbols. We answer this question in the negative. On the other hand, we show that the essential norm of a Toeplitz operator with a continuous symbol is less than or equal to twice the supremum norm of the symbol and prove more precise $p$-dependent estimates. We also discuss some open questions related to the above estimates.