Linear graph transformations on spaces of analytic functions

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.

• Författare: Alexandru Aleman; Karl-Mikael Perfekt; Stefan Richter; Carl Sundberg
• Avdelning/ar: Matematik (naturvetenskapliga fakulteten)
• Publiceringsår: 2015
• Språk: Engelska
• Sidor: 2707-2734
• Publikation/Tidskrift/Serie: Journal of Functional Analysis
• Volym: 268
• Issue: 9
• Länkar: http://dx.doi.org/10.1016/j.jfa.2015.01.012
• Dokumenttyp: Artikel i tidskrift
• Förlag: Elsevier
• Ämne: Mathematics
• Nyckelord: Transitive algebras; Invariant subspaces; Bergman space
• Status: Published
• ISBN/ISSN/Övrigt: ISSN: 0022-1236