On the essential norms of Toeplitz operators with continuous symbols

Eugene Shargorodsky

doi:10.1016/j.jfa.2020.108835

On the essential norms of Toeplitz operators with continuous symbols

Eugene Shargorodsky

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

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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].

Original language	English
Article number	108835
Journal	JOURNAL OF FUNCTIONAL ANALYSIS
Volume	280
Issue number	2
Early online date	27 Oct 2020
DOIs	https://doi.org/10.1016/j.jfa.2020.108835
Publication status	Published - 15 Jan 2021

Keywords

Bounded compact approximation property
Essential norm
Measure of noncompactness
Toeplitz operator

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10.1016/j.jfa.2020.108835

On the essential norms_SHARGORODSKY_Accepted16October2020Publishedonline27October2020_GREEN AAM (CC BY-NC-ND)Accepted author manuscript, 242 KB

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On the essential norms of Toeplitz operators with continuous symbols

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