Bulletin of the Belgian Mathematical Society - Simon Stevin

Analytic Toeplitz operators on the Hardy space $H^p $: a survey

Dragan Vukotić

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Toeplitz operators on Hardy spaces $H\sp{p} $ have been studied extensively during the past 40 years or so. An important special case is that of the operators of multiplication by a bounded analytic function $\f $: $M\sb{\f}(f)=\f f $ (analytic Toeplitz operators). However, many results about them are either only formulated in the case $p=2 $, or are not so easy to find in an explicit form. The purpose of this paper is to give a complete overview of the spectral theory of these analytic Toeplitz operators on a general space $H\sp{p} $, $1\le p <\infty $. The treatment is kept as elementary as possible, placing a special emphasis on the key role played by certain extremal functions related to the Poisson kernel.

Article information

Bull. Belg. Math. Soc. Simon Stevin, Volume 10, Number 1 (2003), 101-113.

First available in Project Euclid: 10 March 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15] 30H05: Bounded analytic functions

Hardy spaces analytic Toeplitz operator essential norm spectrum Fredholm operator


Vukotić, Dragan. Analytic Toeplitz operators on the Hardy space $H^p $: a survey. Bull. Belg. Math. Soc. Simon Stevin 10 (2003), no. 1, 101--113. doi:10.36045/bbms/1047309417. https://projecteuclid.org/euclid.bbms/1047309417

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