Linear graph transformations on spaces of analytic functions

Research output: Contribution to journalArticle


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.


Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics


  • Transitive algebras, Invariant subspaces, Bergman space
Original languageEnglish
Pages (from-to)2707-2734
JournalJournal of Functional Analysis
Issue number9
Publication statusPublished - 2015
Publication categoryResearch