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Linear graph transformations on spaces of analytic functions

Aleman, Alexandru LU ; Perfekt, Karl-Mikael; Richter, Stefan and Sundberg, Carl (2015) In Journal of Functional Analysis 268(9). p.2707-2734
Abstract
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... (More)
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. (Less)
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author
organization
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Contribution to journal
publication status
published
subject
keywords
Transitive algebras, Invariant subspaces, Bergman space
in
Journal of Functional Analysis
volume
268
issue
9
pages
2707 - 2734
publisher
Elsevier
external identifiers
  • wos:000352465500008
  • scopus:84932196279
ISSN
0022-1236
DOI
10.1016/j.jfa.2015.01.012
language
English
LU publication?
yes
id
fc0db482-2b76-46a7-92e9-0d4301610f7d (old id 5402819)
date added to LUP
2015-05-19 13:48:46
date last changed
2017-01-01 05:44:36
@article{fc0db482-2b76-46a7-92e9-0d4301610f7d,
  abstract     = {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.},
  author       = {Aleman, Alexandru and Perfekt, Karl-Mikael and Richter, Stefan and Sundberg, Carl},
  issn         = {0022-1236},
  keyword      = {Transitive algebras,Invariant subspaces,Bergman space},
  language     = {eng},
  number       = {9},
  pages        = {2707--2734},
  publisher    = {Elsevier},
  series       = {Journal of Functional Analysis},
  title        = {Linear graph transformations on spaces of analytic functions},
  url          = {http://dx.doi.org/10.1016/j.jfa.2015.01.012},
  volume       = {268},
  year         = {2015},
}