Linear graph transformations on spaces of analytic functions
(2015) In Journal of Functional Analysis 268(9). p.27072734 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... (More)
 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. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/5402819
 author
 Aleman, Alexandru ^{LU} ; Perfekt, KarlMikael ; 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
 00221236
 DOI
 10.1016/j.jfa.2015.01.012
 language
 English
 LU publication?
 yes
 id
 fc0db4822b7646a792e90d4301610f7d (old id 5402819)
 date added to LUP
 20160401 13:34:09
 date last changed
 20220127 19:53:03
@article{fc0db4822b7646a792e90d4301610f7d, 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.}}, author = {{Aleman, Alexandru and Perfekt, KarlMikael and Richter, Stefan and Sundberg, Carl}}, issn = {{00221236}}, keywords = {{Transitive algebras; Invariant subspaces; Bergman space}}, language = {{eng}}, number = {{9}}, pages = {{27072734}}, 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}}, }