Advertisement

Cyclic invariant subspaces

  • Alexandru Aleman
  • William T. Ross
  • Nathan S. Feldman
Chapter
Part of the Frontiers in Mathematics book series (FM)

Abstract

If M is an invariant subspace of H2 (G), the proof of Corollary 6.1.6. shows that \( \mathcal{N}: = C_{\alpha ^{ - 1} } \circ \mathcal{M}\) is a nearly invariant subspace of Open image in new window . We know from Corollary 3.2.9 that if {0, ∞} is not a subset of the common zeros of N and Φ and Ψ are the normalized reproducing kernels at z=0 and z=∞, then the smallest nearly invariant subspace containing Φ and Ψ is equal to N. From Remark 6.2.12 we also see that Φ ○ α is the normalized reproducing kernel for M at α1(0) while Ψ ○ α is the normalized reproducing kernel at α−1(∞).

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser Verlag AG 2009

Authors and Affiliations

  • Alexandru Aleman
    • 1
  • William T. Ross
    • 2
  • Nathan S. Feldman
    • 3
  1. 1.Centre for Mathematical SciencesLund UniversityLundSweden
  2. 2.Department of Mathematics and Computer ScienceUniversity of RichmondRichmondUSA
  3. 3.Department of MathematicsWashington & Lee UniversityLexingtonUSA

Personalised recommendations