Functions of operators and their commutators in perturbation theory

Yu. Farforovskaya

Banach Center Publications (1994)

  • Volume: 30, Issue: 1, page 147-159
  • ISSN: 0137-6934

Abstract

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This paper shows some directions of perturbation theory for Lipschitz functions of selfadjoint and normal operators, without giving precise proofs. Some of the ideas discussed are explained informally or for the finite-dimensional case. Several unsolved problems are mentioned.

How to cite

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Farforovskaya, Yu.. "Functions of operators and their commutators in perturbation theory." Banach Center Publications 30.1 (1994): 147-159. <http://eudml.org/doc/262700>.

@article{Farforovskaya1994,
abstract = {This paper shows some directions of perturbation theory for Lipschitz functions of selfadjoint and normal operators, without giving precise proofs. Some of the ideas discussed are explained informally or for the finite-dimensional case. Several unsolved problems are mentioned.},
author = {Farforovskaya, Yu.},
journal = {Banach Center Publications},
keywords = {perturbation theory for Lipschitz functions of selfadjoint and normal operators},
language = {eng},
number = {1},
pages = {147-159},
title = {Functions of operators and their commutators in perturbation theory},
url = {http://eudml.org/doc/262700},
volume = {30},
year = {1994},
}

TY - JOUR
AU - Farforovskaya, Yu.
TI - Functions of operators and their commutators in perturbation theory
JO - Banach Center Publications
PY - 1994
VL - 30
IS - 1
SP - 147
EP - 159
AB - This paper shows some directions of perturbation theory for Lipschitz functions of selfadjoint and normal operators, without giving precise proofs. Some of the ideas discussed are explained informally or for the finite-dimensional case. Several unsolved problems are mentioned.
LA - eng
KW - perturbation theory for Lipschitz functions of selfadjoint and normal operators
UR - http://eudml.org/doc/262700
ER -

References

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  3. [3] M. Sh. Birman and M. Z. Solomyak, Double Stieltjes operator integrals, in: Probl. Mat. Fiz. 1, Leningrad Univ., 1966, 33-67 (in Russian). Zbl0161.34602
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  10. [10] E. B. Davies, Lipschitz continuity of functions of operators in the Schatten classes, J. London Math. Soc. 37 (1988), 148-157. Zbl0648.47011
  11. [11] Yu. B. Farforovskaya, An example of a Lipschitz function of a selfadjoint operator giving a non-nuclear increment under a nuclear perturbation, Zap. Nauchn. Sem. LOMI 39 (1974), 194-195 (in Russian). 
  12. [12] Yu. B. Farforovskaya, An estimate of the norm ∥f(A) - f(B)∥ for selfadjoint operators A and B, ibid. 56 (1976), 143-162 (in Russian). 
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  20. [20] A. McIntosh, Counterexample to a question on commutators, Proc. Amer. Math. Soc. 29 (1971), 337-340. Zbl0217.45503
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  23. [23] V. V. Peller, Hankel operators and differentiability properties of functions of selfadjoint (unitary) operators, preprint LOMI, Leningrad, 1984. 
  24. [24] V. V. Peller, Hankel operators in the theory of perturbations of unitary and selfadjoint operators, Funktsional. Anal. i Prilozhen. 19 (2) (1985), 37-51 (in Russian). 
  25. [25] V. V. Peller, For which f does A - B S p imply that f ( A ) - f ( B ) S p ?, in: Oper. Theory: Adv. Appl. 24, Birkhäuser, 1987, 289-294. 
  26. [26] D. Voiculescu, Asymptotically commuting finite rank unitary operators without commuting approximation, Acta Sci. Math. (Szeged) 45 (1983), 429-431. Zbl0538.47003

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