Invariant subspaces of finite codimension in Banach spaces of analytic functions |
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Authors: | Marcus Carlsson |
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Institution: | Purdue University, 150 N. University St., W. Lafayette, IN 47907, United States |
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Abstract: | 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 C2-boundary. |
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Keywords: | Vector-valued analytic functions Invariant subspaces Several variables Bergman space Analytic Hilbert modules |
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