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Linear graph transformations on spaces of analytic functions

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Author

Summary, in English

Let H be a Hilbert space of analytic functions with multiplier algebra M(H), and let M = {(f, T(1)f, ... ,T(n-1)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 vector-subspace, T-i : D -> H are linear transformations that commute with each multiplication operator M-phi is an element of M(H), and M is closed in H-(n). In this paper we investigate the existence of non-trivial 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 L-0,(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.

Publishing year

2015

Language

English

Pages

2707-2734

Publication/Series

Journal of Functional Analysis

Volume

268

Issue

9

Document type

Journal article

Publisher

Elsevier

Topic

  • Mathematics

Keywords

  • Transitive algebras
  • Invariant subspaces
  • Bergman space

Status

Published

ISBN/ISSN/Other

  • ISSN: 0022-1236