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Title of article :
Invariant subspaces of finite codimension in Banach spaces of analytic functions
Author/Authors :
Carlsson، نويسنده , , Marcus، نويسنده ,
Issue Information :
دوهفته نامه با شماره پیاپی سال 2011
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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 C 2 -boundary.
Keywords :
Vector-valued analytic functions , Invariant subspaces , Bergman Space , Analytic Hilbert modules , Several variables
Journal title :
Journal of Mathematical Analysis and Applications
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Link To Document :