The Hardy Space of a Slit Domain

  • Alexandru Aleman
  • William T. Ross
  • Nathan S. Feldman

Part of the Frontiers in Mathematics book series (FM)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Alexandru Aleman, William T. Ross, Nathan S. Feldman
    Pages 1-7
  3. Alexandru Aleman, William T. Ross, Nathan S. Feldman
    Pages 9-23
  4. Alexandru Aleman, William T. Ross, Nathan S. Feldman
    Pages 25-46
  5. Alexandru Aleman, William T. Ross, Nathan S. Feldman
    Pages 47-57
  6. Alexandru Aleman, William T. Ross, Nathan S. Feldman
    Pages 59-63
  7. Alexandru Aleman, William T. Ross, Nathan S. Feldman
    Pages 65-77
  8. Alexandru Aleman, William T. Ross, Nathan S. Feldman
    Pages 79-83
  9. Alexandru Aleman, William T. Ross, Nathan S. Feldman
    Pages 85-91
  10. Alexandru Aleman, William T. Ross, Nathan S. Feldman
    Pages 93-96
  11. Alexandru Aleman, William T. Ross, Nathan S. Feldman
    Pages 97-112
  12. Alexandru Aleman, William T. Ross, Nathan S. Feldman
    Pages 113-114
  13. Back Matter
    Pages 115-124

About this book

Introduction

If H is a Hilbert space and T : H ? H is a continous linear operator, a natural question to ask is: What are the closed subspaces M of H for which T M ? M? Of course the famous invariant subspace problem asks whether or not T has any non-trivial invariant subspaces. This monograph is part of a long line of study of the invariant subspaces of the operator T = M (multiplication by the independent variable z, i. e. , M f = zf )on a z z Hilbert space of analytic functions on a bounded domain G in C. The characterization of these M -invariant subspaces is particularly interesting since it entails both the properties z of the functions inside the domain G, their zero sets for example, as well as the behavior of the functions near the boundary of G. The operator M is not only interesting in its z own right but often serves as a model operator for certain classes of linear operators. By this we mean that given an operator T on H with certain properties (certain subnormal operators or two-isometric operators with the right spectral properties, etc. ), there is a Hilbert space of analytic functions on a domain G for which T is unitarity equivalent to M .

Keywords

Hardy Space Invariant Invariant subspace Multiplication Slit plane character essential spectrum function functional functional analysis functions knowledge model operator

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

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0346-0098-9
  • Copyright Information Birkhäuser Basel 2009
  • Publisher Name Birkhäuser Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-0346-0097-2
  • Online ISBN 978-3-0346-0098-9
  • Series Print ISSN 1660-8046
  • About this book