Operator identities for standard weighted Bergman shift and Toeplitz operators
Author
Summary, in English
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.
Department/s
Publishing year
2013
Language
English
Pages
451-475
Publication/Series
Journal of Operator Theory
Volume
70
Issue
2
Links
Document type
Journal article
Publisher
Theta Foundation
Topic
- Mathematics
Status
Inpress
ISBN/ISSN/Other
- ISSN: 0379-4024