Invariant subspaces with finite codimension in Bergman spaces

Summary, in English

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.

• Author: Alexandru Aleman
• Publishing year: 1992
• Language: English
• Pages: 531-544
• Publication/Series: Transactions of the American Mathematical Society
• Volume: 330
• Issue: 2
• Links: http://www.jstor.org/stable/pdfplus/2153921.pdf
• Document type: Journal article
• Publisher: American Mathematical Society (AMS)
• Topic: Mathematics
• Status: Published
• ISBN/ISSN/Other: ISSN: 0002-9947