Journal of Soviet Mathematics

, Volume 31, Issue 1, pp 2744–2745 | Cite as

Estimate of the norm ∥f(A1, A2)-f(B1, B2)∥ for pairs of self-adjoint commuting operators

  • Yu. B. Farforovskaya


In this note we announce the estimate for the difference mentioned in the title
, where
are the lengths of intervals containing the spectra of the operators A1, B2 and A2, B2; the function f is from the class Lip 1 (with constant 1). The outline of the proof of this estimate is given.

Literature cited

  1. 1.
    Yu. B. Farforovskaya, “Estimate of the norm ¦f(B)-f(A)¦ for self-adjoint operators A and B,” in: Investigations on Linear Operators and Function Theory, J. Sov. Math.,14, No. 2 (1980).Google Scholar
  2. 2.
    Yu. B. Farforovskaya, “The difference f(B)-f(A) for unbounded self-adjoint operators in the theory of perturbations,” in: Investigations on Linear Operators and Function Theory [in Russian], Vol. 10, Zap. Nauchn. Semin. LOMI,107, 213–221 (1982).Google Scholar
  3. 3.
    N. I. Akhiezer and I. M. Glazman, Theory of Linear Operators in Hilbert Space, Ungar Press.Google Scholar
  4. 4.
    Yu. B. Farforovskaya, “Estimate of the closeness of spectral decompositions of selfadjoint operators in the Kantorovich-Rubinshtein metric,” Vestn. Leningr. Gos. Univ., No. 19, Mat., Mekh. Astron.,4, 155–156 (1967).Google Scholar

Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • Yu. B. Farforovskaya

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