Advanced

Characterizations of Bergman space Toeplitz operators with harmonic symbols

Olofsson, Anders LU and Issam, Louhichi (2008) In Journal für Die Reine und Angewandte Mathematik 2008(617). p.1-26
Abstract
It is well-known that Toeplitz operators on the Hardy space of the unit disc are characterized by the equality , where S1 is the Hardy shift operator. In this paper we give a generalized equality of this type which characterizes Toeplitz operators with harmonic symbols in a class of standard weighted Bergman spaces of the unit disc containing the Hardy space and the unweighted Bergman space. The operators satisfying this equality are also naturally described using a slightly extended form of the Sz.-Nagy-Foias functional calculus for contractions. This leads us to consider Toeplitz operators as integrals of naturally associated positive operator measures in order to take properties of balayage into account.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal für Die Reine und Angewandte Mathematik
volume
2008
issue
617
pages
1 - 26
publisher
De Gruyter
external identifiers
  • scopus:45149134403
ISSN
0075-4102
DOI
10.1515/CRELLE.2008.024
language
English
LU publication?
yes
id
2d6fc106-3c4d-4f3d-a868-12ba1228fc6f (old id 1397843)
date added to LUP
2009-05-19 14:47:05
date last changed
2017-01-01 05:07:50
@article{2d6fc106-3c4d-4f3d-a868-12ba1228fc6f,
  abstract     = {It is well-known that Toeplitz operators on the Hardy space of the unit disc are characterized by the equality , where S1 is the Hardy shift operator. In this paper we give a generalized equality of this type which characterizes Toeplitz operators with harmonic symbols in a class of standard weighted Bergman spaces of the unit disc containing the Hardy space and the unweighted Bergman space. The operators satisfying this equality are also naturally described using a slightly extended form of the Sz.-Nagy-Foias functional calculus for contractions. This leads us to consider Toeplitz operators as integrals of naturally associated positive operator measures in order to take properties of balayage into account.},
  author       = {Olofsson, Anders and Issam, Louhichi},
  issn         = {0075-4102},
  language     = {eng},
  number       = {617},
  pages        = {1--26},
  publisher    = {De Gruyter},
  series       = {Journal für Die Reine und Angewandte Mathematik},
  title        = {Characterizations of Bergman space Toeplitz operators with harmonic symbols},
  url          = {http://dx.doi.org/10.1515/CRELLE.2008.024},
  volume       = {2008},
  year         = {2008},
}