Skip to main content
SpringerLink
Log in

Relaxed Commutant Lifting: An Equivalent Version and a New Application

  • Conference paper
Recent Advances in Operator Theory and Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 187))

Abstract

This paper presents a few additions to commutant lifting theory. An operator interpolation problem is introduced and shown to be equivalent to the relaxed commutant lifting problem. Using this connection a description of all solutions of the former problem is given. Also a new application, involving bounded operators induced by H 2 operator-valued functions, is presented.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D. Alpay, V. Bolotnikov, and Ph. Loubaton, On tangential H 2 interpolation with second-order norm constraints, Integral Equations and Operator Theory 24 (1996), 156–178.

    Article  MATH  MathSciNet  Google Scholar 

  2. D. Alpay, V. Bolotnikov, and Ph. Loubaton, On interpolation for Hardy functions in a certain class of domains under moment type constraints, Houston Journal of Mathematics, No. 3 (1997), Vol. 23, 539–571.

    MATH  MathSciNet  Google Scholar 

  3. C. Foias and A. E. Frazho, The Commutant Lifting Approach to Interpolation Problems, Operator Theory: Advances and Applications, 44, Birkhäuser-Verlag, Basel, 1990.

    Google Scholar 

  4. C. Foias, A.E. Frazho, and M.A. Kaashoek, Relaxation of metric constrained interpolation and a new lifting theorem, Integral Equations and Operator Theory, 42 (2002), 253–310.

    Article  MATH  MathSciNet  Google Scholar 

  5. A.E. Frazho, S. ter Horst, and M.A. Kaashoek, Coupling and relaxed commutant lifting, Integral Equations and Operator Theory, 54 (2006), 33–67.

    Article  MATH  MathSciNet  Google Scholar 

  6. A.E. Frazho, S. ter Horst, and M.A. Kaashoek, All solutions to the relaxed commutant lifting problem, Acta Sci. Math (Szegged) 72 (2006), 299–318.

    MATH  Google Scholar 

  7. S. ter Horst, Relaxed commutant lifting and a relaxed Nehari problem: Redheffer state space formulas, Math. Nachr., to appear.

    Google Scholar 

  8. B. Sz.-Nagy and C. Foias, Harmonic Analysis of Operators on Hilbert Space, North Holland Publishing Co., Amsterdam-Budapest, 1970.

    Google Scholar 

  9. D. Sarason, Exposed points in H 1. I, in: The Gohberg anniversary collection, Vol. II, OT 41, Birkhäuser Verlag, Basel, 1989, pp. 485–496.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Aeronautics and Astronautics, Purdue University, West Lafayette, IN, 47907, USA

    A. E. Frazho

  2. Afdeling Wiskunde, Faculteit der Exacte Wetenschappen, Vrije Universiteit, De Boelelaan 1081a, 1081 HV, Amsterdam, The Netherlands

    S. ter Horst & M. A. Kaashoek

Authors
  1. A. E. Frazho
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. ter Horst
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. A. Kaashoek
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Tsuyoshi Ando, Hokkaido University (Emeritus), Sapporo, Japan

    Tsuyoshi Ando

  2. Department of Mathematics, University of Iowa, Iowa City, IA, 52242, USA

    RaĂşl E. Curto

  3. Department of Mathematics, Kyungpook National University, Daegu, 702-701, Korea

    Il Bong Jung

  4. Department of Mathematics, Seoul National University, Seoul, 151-747, Korea

    Woo Young Lee

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Birkhäuser Verlag Basel/Switzerland

About this paper

Cite this paper

Frazho, A.E., ter Horst, S., Kaashoek, M.A. (2008). Relaxed Commutant Lifting: An Equivalent Version and a New Application. In: Ando, T., Curto, R.E., Jung, I.B., Lee, W.Y. (eds) Recent Advances in Operator Theory and Applications. Operator Theory: Advances and Applications, vol 187. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8893-5_8

Download citation

Publish with us

Policies and ethics

Search

Navigation