Invariant subspaces of finite codimension in Banach spaces of analytic functions

We give a characterization of invariant subspaces of finite codimension in Banach spaces of vector-valued analytic functions in several variables, where invariant refers to invariance under multiplication by any polynomial. We obtain very weak conditions under which our characterization applies, tha...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications Vol. 373; no. 1; pp. 1 - 12
Main Author: Carlsson, Marcus
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Inc 2011
Elsevier
Subjects:
Analytic Hilbert modules
Bergman space
Exact sciences and technology
Functional analysis
Global analysis, analysis on manifolds
Invariant subspaces
Mathematical analysis
Mathematics
Operator theory
Sciences and techniques of general use
Several complex variables and analytic spaces
Several variables
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Vector-valued analytic functions
Bergman space
Invariant subspaces
Several variables
Vector-valued analytic functions
Analytic Hilbert modules
Polynomial
Invariant
Multiplication
Invariant subspace
Invariance
Banach space
Vector space
Mathematical analysis
Analytic space
Analytical function
ISSN:0022-247X, 1096-0813
Online Access:Get full text
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Summary:We give a characterization of invariant subspaces of finite codimension in Banach spaces of vector-valued analytic functions in several variables, where invariant refers to invariance under multiplication by any polynomial. We obtain very weak conditions under which our characterization applies, that unifies and improves a number of previous results. In the vector-valued case, the results are new even for one complex variable. As a concrete application in several variables, we consider the Bergman space on a strictly pseudo-convex domain, and we improve previous results (assuming C ∞ -boundary) to the case of C 2 -boundary.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2010.06.001