An operator identity for standard weighted Bergman shift operators
(2011) In Bachelor's Theses in Mathematical Sciences MATX01 20111Mathematics (Faculty of Sciences)
- Abstract
- We consider the scale of standard weighted Bergman spaces in the unit disc. We show that in this scale of spaces the shift operator satisfies a certain operator identity. By duality arguments this operator identity leads to an operator inequality for the Bergman shift operator in the parameter range $-1<\alpha\leqq0$. In the special case $\alpha=0$ the operator inequality obtained coincides with that of Shimorin.
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/2517892
- author
- Wennman, Aron LU
- supervisor
- organization
- course
- MATX01 20111
- year
- 2011
- type
- M2 - Bachelor Degree
- subject
- publication/series
- Bachelor's Theses in Mathematical Sciences
- report number
- LUNFMA-4011-2011
- ISSN
- 1654-6229
- language
- English
- id
- 2517892
- date added to LUP
- 2014-12-15 14:11:24
- date last changed
- 2018-10-11 16:22:28
@misc{2517892, abstract = {{We consider the scale of standard weighted Bergman spaces in the unit disc. We show that in this scale of spaces the shift operator satisfies a certain operator identity. By duality arguments this operator identity leads to an operator inequality for the Bergman shift operator in the parameter range $-1<\alpha\leqq0$. In the special case $\alpha=0$ the operator inequality obtained coincides with that of Shimorin.}}, author = {{Wennman, Aron}}, issn = {{1654-6229}}, language = {{eng}}, note = {{Student Paper}}, series = {{Bachelor's Theses in Mathematical Sciences}}, title = {{An operator identity for standard weighted Bergman shift operators}}, year = {{2011}}, }