Nearly invariant subspaces

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


For a general domain Open image in new window , a subspace1 NH2 (Ω) (not necessarily invariant) is said to be nearly invariant if there is some λ0 ∈ Ω such that whenever fN and f0) = 0, then
$$ \frac{f} {{z - \lambda _0 }} \in N. $$
The following useful proposition, found in [7, Prop. 5.1], says that we need not single out a particular λ0.


Invariant Subspace Toeplitz Operator Extremal Function Common Zero Linear Manifold 
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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

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