Perturbation of the spectrum οf an essentially selfadjoint operator

Andrzej Pokrzywa

Applicationes Mathematicae (1993)

  • Volume: 22, Issue: 1, page 75-89
  • ISSN: 1233-7234

Abstract

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The aim of this paper is to find estimates of the Hausdorff distance between the spectra of two nonselfadjoint operators. The operators considered are assumed to have their imaginary parts in some normed ideal of compact operators. In the case of the classical Schatten ideals the estimates are given explicitly.

How to cite

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Pokrzywa, Andrzej. "Perturbation of the spectrum οf an essentially selfadjoint operator." Applicationes Mathematicae 22.1 (1993): 75-89. <http://eudml.org/doc/219085>.

@article{Pokrzywa1993,
abstract = {The aim of this paper is to find estimates of the Hausdorff distance between the spectra of two nonselfadjoint operators. The operators considered are assumed to have their imaginary parts in some normed ideal of compact operators. In the case of the classical Schatten ideals the estimates are given explicitly.},
author = {Pokrzywa, Andrzej},
journal = {Applicationes Mathematicae},
keywords = {crossnorm; spectrum; Hausdorff distance between the spectra of two nonselfadjoint operators; normed ideal of compact operators; Schatten ideals},
language = {eng},
number = {1},
pages = {75-89},
title = {Perturbation of the spectrum οf an essentially selfadjoint operator},
url = {http://eudml.org/doc/219085},
volume = {22},
year = {1993},
}

TY - JOUR
AU - Pokrzywa, Andrzej
TI - Perturbation of the spectrum οf an essentially selfadjoint operator
JO - Applicationes Mathematicae
PY - 1993
VL - 22
IS - 1
SP - 75
EP - 89
AB - The aim of this paper is to find estimates of the Hausdorff distance between the spectra of two nonselfadjoint operators. The operators considered are assumed to have their imaginary parts in some normed ideal of compact operators. In the case of the classical Schatten ideals the estimates are given explicitly.
LA - eng
KW - crossnorm; spectrum; Hausdorff distance between the spectra of two nonselfadjoint operators; normed ideal of compact operators; Schatten ideals
UR - http://eudml.org/doc/219085
ER -

References

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  1. [1] R. Bhatia and K. K. Mukherjea, On the rate of change of spectra of operators, Linear Algebra Appl. 27 (1979), 147-157. Zbl0421.15019
  2. [2] L. Elsner, An optimal bound for spectral variation of two matrices, ibid. 71 (1985), 77-80. Zbl0583.15009
  3. [3] I. C. Gohberg and M. G. Krein, Introduction to the Theory of Linear Non-Selfadjoint Operators, Nauka, Moscow, 1965 (in Russian). Zbl0138.07803
  4. [3] I. C. Gohberg and M. G. Krein-, Theory of Volterra Operators and Its Applications, Nauka, Moscow, 1967 (in Russian). Zbl0194.43804
  5. [5] T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin, 1966. 
  6. [6] A. Pokrzywa, Spectra of operators with fixed imaginary parts, Proc. Amer. Math. Soc. 81 (1981), 359-364. Zbl0477.15007
  7. [7] A. Pokrzywa, On continuity of spectra in norm ideals, Linear Algebra Appl. 69 (1985), 121-130. Zbl0581.47013
  8. [8] Mathematica, Version 2.0, Wolfram Research, Inc., Champaign, Ill., 1991. 

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