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An operator identity for standard weighted Bergman shift operators

Wennman, Aron LU (2011) In Bachelor's Thesis in Mathematical Sciences MATX01 20111
Mathematics (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.
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author
Wennman, Aron LU
supervisor
organization
course
MATX01 20111
year
type
M2 - Bachelor Degree
subject
publication/series
Bachelor's Thesis 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
2015-09-07 09:04:56
@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 Thesis in Mathematical Sciences},
  title        = {An operator identity for standard weighted Bergman shift operators},
  year         = {2011},
}