Advanced

Operator identities for standard weighted Bergman shift and Toeplitz operators

Wennman, Aron (2011) In Master's Theses in Mathematical Sciences MATM01 20112
Mathematics (Faculty of Sciences)
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
Wennman, Aron
supervisor
organization
course
MATM01 20112
year
type
H2 - Master's Degree (Two Years)
subject
publication/series
Master's Theses in Mathematical Sciences
report number
LUNFMA-3066-2011
ISSN
1404-6342
other publication id
2012:E32
language
English
id
2517775
date added to LUP
2012-09-20 15:48:33
date last changed
2013-01-08 15:12:49
@misc{2517775,
  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       = {Wennman, Aron},
  issn         = {1404-6342},
  language     = {eng},
  note         = {Student Paper},
  series       = {Master's Theses in Mathematical Sciences},
  title        = {Operator identities for standard weighted Bergman shift and Toeplitz operators},
  year         = {2011},
}