Skip to main content

Operator Dilations with Prescribed Commutators

  • Conference paper
Operator Theory, System Theory and Related Topics

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 123))

Abstract

A dilation problem with prescribed commutator for pairs of selfadjoint matrices is related constructively to the truncated moment problems in the plane for positive measures as well as for bounded functions. A series of particular cases of this dilation problem reveals its deep connections with the structure of some classes of semi-normal operators.

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

Access this chapter

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
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
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. Akhiezer, N. I., The classical moment problem and some related questions in analysis, Hafner, New York, 1965.

    MATH  Google Scholar 

  2. Akhiezer, N. I. and Krein, M. G., Some questions in the theory of moments, Transl. Amer. Math. Soc. vol. 2, Providence, R.I., 1962.

    Google Scholar 

  3. Curto, R. and Fialkow, L., Solution of the truncated complex moment problem for flat data, Mem. Amer. Math. Soc. vol. 568, Providence, R.I., 1996.

    Google Scholar 

  4. Carey, R. and Pincus, J. D., Construction of seminormal operators with prescribed mosaic, Indiana Univ. Math. J. 23 (1974), 1155–1165.

    Article  MathSciNet  MATH  Google Scholar 

  5. Gustafsson, B. and Putinar, M., Linear analysis of quadrature domains. II, preprint 1997.

    Google Scholar 

  6. Karlin, S. and Studden, W. J., Tchebycheff systems: with applications in Analysis and Statistics, Interscience Publ., New York, 1966.

    MATH  Google Scholar 

  7. Livšic, M. et al., Theory of commuting nonselfadjoint operators, Kluwer, Dordrecht, 1995.

    MATH  Google Scholar 

  8. Martin, M. and Putinar, M., Lectures on hyponormal operators, Birkhäuser, Basel, 1989.

    Book  MATH  Google Scholar 

  9. McCarthy, J. and Yang, L., Subnormal operators and quadrature domains, Adv. Math. 127 (1997), 52–72.

    Article  MathSciNet  MATH  Google Scholar 

  10. Mysovskikh, I. P., Interpolatory cubature formulas (in Russian), Nauka, Moscow, 1981.

    Google Scholar 

  11. Putinar, M., A dilation theory approach to cubature formulas. II, Math. Nachr., to appear.

    Google Scholar 

  12. Riesz, F. and Sz.-Nagy, B., Functional analysis, Dover, New York, 1990.

    MATH  Google Scholar 

  13. Xia, D., Hyponormal operators with finite-rank self-commutator and quadrature domains, J. Math. Anal. Appl. 203 (1996), 540–559.

    Article  MathSciNet  MATH  Google Scholar 

  14. Xu, Y., On orthogonal polynomials in several variables, Fields Inst. Comm. 14 (Special functions, q-series and related topics, Ismail, M. E. H. et al., eds.), American Mathematical Society, Providence, 1997, pp. 247–270.

    Google Scholar 

  15. Yakubovich, D., Subnormal operators of finite type. I: Xia’s model and real algebraic curves in C2, Rev. Mat. Iberoamericana 14 (1998), 95–115.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer Basel AG

About this paper

Cite this paper

Putinar, M. (2001). Operator Dilations with Prescribed Commutators. In: Alpay, D., Vinnikov, V. (eds) Operator Theory, System Theory and Related Topics. Operator Theory: Advances and Applications, vol 123. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8247-7_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-8247-7_19

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9491-3

  • Online ISBN: 978-3-0348-8247-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics