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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.
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author
and
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
2016-04-01 12:25:21
date last changed
2025-04-04 14:08:44
@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}},
  doi          = {{10.1515/CRELLE.2008.024}},
  volume       = {{2008}},
  year         = {{2008}},
}