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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/5402819
- author
- Aleman, Alexandru LU ; Perfekt, Karl-Mikael ; Richter, Stefan and Sundberg, Carl
- organization
- publishing date
- 2015
- 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)
- date added to LUP
- 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 >= 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}},
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}},
}