Invariant subspaces with finite codimension in Bergman spaces
(1992) In Transactions of the American Mathematical Society 330(2). p.531-544- Abstract
- Let $\Omega$ be a domain in the complex plane. Denote by $L^p_{\roman{a}}(\Omega)$ $(1\le p<+\infty)$ the Bergman space over $\Omega$. The author presents a description of finite codimensional space $E\subset L^p_{\roman{a}}(\Omega)$ such that $zE\subset E$. Under some conditions on $\Omega$ an analogous result is due to \n S. Axler\en and \n P. Bourdon\en [same journal {\bf306} (1988), no. 2, 805--817; MR0933319 (89f:46051)].
For an arbitrary bounded domain in C there are described those finite codimensional subspaces of the Bergman space that are invariant under multiplication by z.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1467372
- author
- Aleman, Alexandru LU
- publishing date
- 1992
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Transactions of the American Mathematical Society
- volume
- 330
- issue
- 2
- pages
- 531 - 544
- publisher
- American Mathematical Society (AMS)
- external identifiers
-
- scopus:84966253530
- ISSN
- 0002-9947
- language
- English
- LU publication?
- no
- id
- 8d2c2fc7-8c32-4ad0-ad07-f11832f31dd1 (old id 1467372)
- alternative location
- http://www.jstor.org/stable/pdfplus/2153921.pdf
- date added to LUP
- 2016-04-01 16:09:19
- date last changed
- 2021-01-03 06:17:32
@article{8d2c2fc7-8c32-4ad0-ad07-f11832f31dd1, abstract = {{Let $\Omega$ be a domain in the complex plane. Denote by $L^p_{\roman{a}}(\Omega)$ $(1\le p<+\infty)$ the Bergman space over $\Omega$. The author presents a description of finite codimensional space $E\subset L^p_{\roman{a}}(\Omega)$ such that $zE\subset E$. Under some conditions on $\Omega$ an analogous result is due to \n S. Axler\en and \n P. Bourdon\en [same journal {\bf306} (1988), no. 2, 805--817; MR0933319 (89f:46051)].<br/><br> <br/><br> For an arbitrary bounded domain in C there are described those finite codimensional subspaces of the Bergman space that are invariant under multiplication by z.}}, author = {{Aleman, Alexandru}}, issn = {{0002-9947}}, language = {{eng}}, number = {{2}}, pages = {{531--544}}, publisher = {{American Mathematical Society (AMS)}}, series = {{Transactions of the American Mathematical Society}}, title = {{Invariant subspaces with finite codimension in Bergman spaces}}, url = {{http://www.jstor.org/stable/pdfplus/2153921.pdf}}, volume = {{330}}, year = {{1992}}, }