Skip to main content
Log in

Hankel operators in the perturbation theory of unitary and self-adjoint operators

  • Published:
Functional Analysis and Its Applications Aims and scope

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature Cited

  1. M. G. Krein, "On some new studies in the perturbation theory of self-adjoint operators," in: First Mathematics Summer School, Part I [in Russian], Naukova Dumka, Kiev (1964), pp. 103–187.

    Google Scholar 

  2. Yu. L. Daletskii and S. G. Krein, "The integration and differentiation of Hermitian operators and appliations to the theory of perturbations," Tr. Sem. Funkts. Anal., Voronezh,1, 81–105 (1956).

    Google Scholar 

  3. M. Sh. Birman and M. Z. Solomyak, "Double Stieltjes operator integrals. III," Probl. Mat. Fiz., No. 6, 27–53 (1973).

    Google Scholar 

  4. M. Sh. Birman and M. Z. Solomyak, "Remarks on the spectral shift function," J. Sov. Math.,3, No. 4 (1975).

  5. M. Sh. Birman and M. Z. Solomyak, "Double Stieltjes operator integrals," Probl. Mat. Fiz., No. 2, 33–67 (1966).

    Google Scholar 

  6. M. Sh. Birman and M. Z. Solomyak, "Double Stieltjes operator integrals. II," Probl. Mat. Fiz., No. 2, 26–60 (1967).

    Google Scholar 

  7. Yu. B. Farforovskaya, "An example of a Lipschitz function of a self-adjoint operator, yielding a nonnuclear increment under a nuclear perturbation," J. Sov. Math.,4, No. 4 (1975).

  8. Yu. B. Farforovskaya, "On the estimation of the difference f(B) — f(A) in theG p classes," J. Sov. Math.,8, No. 1 (1977).

  9. Yu. B. Farforovskaya, "An estimate of the norm |f(B) — f(A)| for self-adjoint operators A and B," J. Sov. Math.,14, No. 2 (1980).

  10. H. Widom, "When are differentiable functions differentiable?," Lect. Notes Math., No. 1043, 184–188 (1984).

    Google Scholar 

  11. V. V. Peller, "Hankel operators of classG p and their applications (rational approximation, Gaussian processes, the problem of majorization of operators)," Mat. Sb.,113, No. 4, 538–581 (1980).

    Google Scholar 

  12. V. V. Peller, Hankel operators and differentiability properties of functions of self-adjoint (unitary) operators. Preprint LOMI, E-1-84, LOMI, Leningrad (1984).

    Google Scholar 

  13. G. Bennett, "Schur multipliers," Duke Math. J.,44, No. 3, 603–639 (1977).

    Google Scholar 

  14. A. Pietsch, Operator Ideals, North-Holland, Amsterdam (1980).

    Google Scholar 

  15. J. Lindenstrauss and A. Pelczynski, "Absolutely summing operators inL p-spaces and their applications," Stud. Math.,29, No. 3, 275–326 (1968).

    Google Scholar 

  16. L. V. Kantorovich and G. P. Akilov, Functional Analysis [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  17. J. Bergh and J. Lofstrom, Interpolation Spaces. An Introduction, Springer-Verlag, Berlin (1976).

    Google Scholar 

  18. E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press (1970).

  19. J. Peetre, New Thoughts on Besov Spaces, Duke Univ. Math. Ser. I, Math. Dept. of Duke Univ., Durham (1976).

    Google Scholar 

  20. A. B. Aleksandrov, "Essays on nonlocally convex Hardy classes," Lect. Notes Math., No. 864, 1–89 (1981).

    Google Scholar 

  21. E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press (1971).

  22. W. Rudin, "Trigonometric series with gaps," J. Math. Mech.,9, No. 2, 203–227 (1960).

    Google Scholar 

  23. P. Koosis, Introduction to Hp Spaces, Cambridge University Press (1980).

Download references

Authors

Additional information

V. A. Steklov Institute of Mathematics, Leningrad Branch, Academy of Sciences of the USSR. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 19, No. 2, pp. 37–51, April–June, 1985.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Peller, V.V. Hankel operators in the perturbation theory of unitary and self-adjoint operators. Funct Anal Its Appl 19, 111–123 (1985). https://doi.org/10.1007/BF01078390

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01078390

Keywords

Navigation