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

Vukotić, Dragan

Bull. Belg. Math. Soc. Simon Stevin, Tome 10 (2003) no. 1, p. 101-113 / Harvested from Project Euclid

Résumé

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.

Publié le : 2003-01-14
Classification: Hardy spaces, analytic Toeplitz operator, essential norm, spectrum, Fredholm operator, 47B35, 30H05

@article{1047309417,
     author = {Vukoti\'c, Dragan},
     title = {Analytic Toeplitz operators on the Hardy space $H^p $: a survey},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {10},
     number = {1},
     year = {2003},
     pages = { 101-113},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1047309417}
}

Vukotić, Dragan. Analytic Toeplitz operators on the Hardy space $H^p $: a survey. Bull. Belg. Math. Soc. Simon Stevin, Tome 10 (2003) no. 1, pp.  101-113. http://gdmltest.u-ga.fr/item/1047309417/