Skip to main content

Compact Hilbert Space Operators of Order One

  • Chapter
  • First Online:
Completeness Theorems and Characteristic Matrix Functions

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 288))

  • 333 Accesses

Abstract

In this chapter we further specify Theorem 2.2.2 for compact Hilbert space operators of order one. Such operators are Hilbert-Schmidt operators and not necessarily trace class operators. We begin with some remarks about the latter class of operators. Throughout this chapter we shall use terminology and basic facts from the theory of entire functions which can be found in Chap. 14.

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 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 159.99
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

References

  1. A.D. Baranov, D.V. Yakubovich, One-dimensional perturbations of unbounded selfadjoint operators with empty spectrum. J. Math. Anal. Appl. 424, 1404–1424 (2015)

    Article  MathSciNet  Google Scholar 

  2. I.C. Gohberg, M.G. Krein, Introduction to the Theory of Linear Nonselfadjoint Operators (American Mathematical Society, Providence, 1969)

    MATH  Google Scholar 

  3. I. Gohberg, S. Goldberg, M.A. Kaashoek, Classes of Linear Operators I (Birkhäuser Verlag, Basel, 1990)

    Book  Google Scholar 

  4. A.P. Khromov, Finite-dimensional perturbations of Volterra operators. J. Math. Sci. 138, 5593–6066 (2006)

    Article  MathSciNet  Google Scholar 

  5. C. Liaw, S. Treil, Rank one perturbations and singular integral operators. J. Funct. Anal. 257, 1947–1975 (2009)

    Article  MathSciNet  Google Scholar 

  6. A.A. Shkalikov, Perturbations of self-adjoint and normal operators with discrete spectrum. Russ. Math. Surv. 71, 907–964 (2016)

    Article  MathSciNet  Google Scholar 

  7. S.M. Verduyn Lunel, D.V. Yakubovich, A functional model approach to linear neutral functional differential equations. Integr. Equ. Oper. Theory 27, 347–378 (1997)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Kaashoek, M.A., Verduyn Lunel, S.M. (2022). Compact Hilbert Space Operators of Order One. In: Completeness Theorems and Characteristic Matrix Functions. Operator Theory: Advances and Applications, vol 288. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-04508-0_3

Download citation

Publish with us

Policies and ethics