Operator identities for standard weighted Bergman shift and Toeplitz operators
(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:
https://lup.lub.lu.se/record/3242997
- author
- Olofsson, Anders LU and Wennman, Aron LU
- organization
- publishing date
- 2013
- 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}}, }