Linear graph transformations on spaces of analytic functions
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Abstract
Let H be a Hilbert space of analytic functions with multiplier algebra M(H), and let M = {(f, T(1)f, ... ,T(n1)f) : f is an element of D} be an invariant graph subspace for M(H)((n)). Here n >= 2, D subset of H is a vectorsubspace, Ti : D > H are linear transformations that commute with each multiplication operator Mphi is an element of M(H), and M is closed in H(n). In this paper we investigate the existence of nontrivial common invariant subspaces of operator algebras of the type A(M) = {A is an element of B(H) : AD subset of D : AT(i)f = T(i)Af for all f is an element of D}. In particular, for the Bergman space L0,(2) we exhibit examples of invariant graph subspaces of fiber dimension 2 such that A(M) does not have any nontrivial invariant subspaces that are defined by linear relations of the graph transformations for M. (C) 2015 Elsevier Inc. All rights reserved.
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Research areas and keywords  Subject classification (UKÄ) – MANDATORY
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Original language  English 

Pages (fromto)  27072734 
Journal  Journal of Functional Analysis 
Volume  268 
Issue number  9 
Publication status  Published  2015 
Publication category  Research 
Peerreviewed  Yes 