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Operator identities for standard weighted Bergman shift and Toeplitz operators

Olofsson, Anders LU and Wennman, Aron LU (2013) In Journal of Operator Theory 70(2). p.451-475
Abstract
We prove an operator identity for the shift operator in the scale of standard weighted Bergman spaces in the unit disc. This operator identity is then applied in the context of functional calculus for the shift operator and a characterization of harmonic symbol Bergman space Toeplitz operators is obtained generalizing an earlier result by Louhichi and Olofsson. Duality arguments lead to operator inequalities and structure formulas for reproducing kernel functions which make contact with work of Richter, Shimorin, and others.
Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Contribution to journal
publication status
in press
subject
in
Journal of Operator Theory
volume
70
issue
2
pages
451 - 475
publisher
Theta Foundation
external identifiers
  • scopus:84889649765
ISSN
0379-4024
language
English
LU publication?
yes
id
11bd55a3-03a6-4a66-8cc8-25d2c8d75396 (old id 3242997)
alternative location
http://www.maths.lth.se/matematiklu/personal/olofsson/bergmanidentityrev.pdf
date added to LUP
2016-04-01 10:37:06
date last changed
2022-01-26 00:56:25
@article{11bd55a3-03a6-4a66-8cc8-25d2c8d75396,
  abstract     = {{We prove an operator identity for the shift operator in the scale of standard weighted Bergman spaces in the unit disc. This operator identity is then applied in the context of functional calculus for the shift operator and a characterization of harmonic symbol Bergman space Toeplitz operators is obtained generalizing an earlier result by Louhichi and Olofsson. Duality arguments lead to operator inequalities and structure formulas for reproducing kernel functions which make contact with work of Richter, Shimorin, and others.}},
  author       = {{Olofsson, Anders and Wennman, Aron}},
  issn         = {{0379-4024}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{451--475}},
  publisher    = {{Theta Foundation}},
  series       = {{Journal of Operator Theory}},
  title        = {{Operator identities for standard weighted Bergman shift and Toeplitz operators}},
  url          = {{http://www.maths.lth.se/matematiklu/personal/olofsson/bergmanidentityrev.pdf}},
  volume       = {{70}},
  year         = {{2013}},
}