# Lund University Publications

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### Linear graph transformations on spaces of analytic functions

(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)
author
; ; and
organization
publishing date
type
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)
2016-04-01 13:34:09
date last changed
2022-01-27 19:53:03
```@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 &gt;= 2, D subset of H is a vector-subspace, T-i : D -&gt; 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}},
keywords     = {{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}},
doi          = {{10.1016/j.jfa.2015.01.012}},
volume       = {{268}},
year         = {{2015}},
}

```