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Invariant subspaces with finite codimension in Bergman spaces

Aleman, Alexandru LU (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.
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author
publishing date
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)
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
2009-09-16 13:58:06
date last changed
2016-06-29 09:16:29
@article{8d2c2fc7-8c32-4ad0-ad07-f11832f31dd1,
  abstract     = {Let $\Omega$ be a domain in the complex plane. Denote by $L^p_{\roman{a}}(\Omega)$ $(1\le p&lt;+\infty)$ 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},
  volume       = {330},
  year         = {1992},
}