## Bulletin of the Belgian Mathematical Society - Simon Stevin

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

Dragan Vukotić

#### Abstract

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

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

Dates
First available in Project Euclid: 10 March 2003

https://projecteuclid.org/euclid.bbms/1047309417

Digital Object Identifier
doi:10.36045/bbms/1047309417

Mathematical Reviews number (MathSciNet)
MR2032329

Zentralblatt MATH identifier
1039.47016

#### Citation

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