Invariant subspaces of finite codimension in Banach spaces of analytic functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:373

Article

Carlsson, Marcus

关键词: Vector-valued analytic functions;    Invariant subspaces;    Several variables;    Bergman space;    Analytic Hilbert modules;   

DOI  :  10.1016/j.jmaa.2010.06.001

来源: Elsevier

【 摘 要 】

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(infinity)-boundary) to the case of C(2)-boundary. (c) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free