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On the essential norms of Toeplitz operators with continuous symbols

Research output: Contribution to journalArticle

Original languageEnglish
Article number108835
JournalJOURNAL OF FUNCTIONAL ANALYSIS
Volume280
Issue number2
Early online date27 Oct 2020
DOIs
Accepted/In press16 Oct 2020
E-pub ahead of print27 Oct 2020
Published15 Jan 2021

King's Authors

Abstract

It is well known that the essential norm of a Toeplitz operator on the Hardy space H p(T), 1<p<∞ is greater than or equal to the L (T) norm of its symbol. In 1988, A. Böttcher, N. Krupnik, and B. Silbermann posed the question on whether or not 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 T(a) with a continuous symbol a is less than or equal to [Formula presented].

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