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1993 | 106 | 2 | 153-174
Tytuł artykułu

Perturbation theory relative to a Banach algebra of operators

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Języki publikacji
EN
Abstrakty
EN
Let ℬ be a Banach algebra of bounded linear operators on a Banach space X. Let S be a closed linear operator in X, and let R be a linear operator in X. In this paper the spectral and Fredholm theory relative to ℬ of the perturbed operator S + R is developed. In particular, the situation where R is S-inessential relative to ℬ is studied. Several examples are given to illustrate the usefulness of these concepts.
Czasopismo
Rocznik
Tom
106
Numer
2
Strony
153-174
Opis fizyczny
Daty
wydano
1993
otrzymano
1992-06-02
poprawiono
1993-03-16
Twórcy
  • Department of Mathematics, University of Oregon, Eugene, Oregon 97403, U.S.A.
Bibliografia
  • [1] W. Arendt and A. Sourour, Perturbation of regular operators and the order essential spectrum, Nederl. Akad. Wetensch. Proc. 89 (1986), 109-122.
  • [2] B. Barnes, Fredholm theory in a Banach algebra of operators, Proc. Roy. Irish Acad. 87A (1987), 1-11.
  • [3] B. Barnes, The spectral and Fredholm theory of extensions of bounded linear operators, Proc. Amer. Math. Soc. 105 (1989), 941-949.
  • [4] B. Barnes, Interpolation of spectrum of bounded operators on Lebesgue spaces, Rocky Mountain J. Math. 20 (1990), 359-378.
  • [5] B. Barnes, Essential spectra in a Banach algebra applied to linear operators, Proc. Roy. Irish Acad. 90A (1990), 73-82.
  • [6] B. Barnes, Closed operators affiliated with a Banach algebra of operators, Studia Math. 101 (1992), 215-240.
  • [7] B. Barnes, G. Murphy, R. Smyth, and T. T. West, Riesz and Fredholm Theory in Banach Algebras, Pitman Res. Notes in Math. 67, Pitman, Boston 1982.
  • [8] F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, Berlin 1973.
  • [9] H. G. Dales, On norms on algebras, in: Proc. Centre Math. Anal. Austral. Nat. Univ.21, 1989, 61-95.
  • [10] N. Dunford and J. Schwartz, Linear Operators, Part I, Interscience, New York 1964.
  • [11] S. Goldberg, Unbounded Linear Operators, McGraw-Hill, New York 1966.
  • [12] K. Jörgens, Linear Integral Operators, Pitman, Boston 1982.
  • [13] T. Kato, Perturbation Theory for Linear Operators, Springer, New York 1966.
  • [14] D. Kleinecke, Almost-finite, compact, and inessential operators, Proc. Amer. Math. Soc. 14 (1963), 863-868.
  • [15] R. Kress, Linear Integral Equations, Springer, Berlin 1989.
  • [16] W. Pfaffenberger, On the ideals of strictly singular and inessential operators, Proc. Amer. Math. Soc. 25 (1970), 603-607.
  • [17] M. Schechter, Principles of Functional Analysis, Academic Press, New York 1971.
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bwmeta1.element.bwnjournal-article-smv106i2p153bwm
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