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1995 | 114 | 1 | 13-27
Tytuł artykułu

Operational quantities characterizing semi-Fredholm operators

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Several operational quantities have appeared in the literature characterizing upper semi-Fredholm operators. Here we show that these quantities can be divided into three classes, in such a way that two of them are equivalent if they belong to the same class, and are comparable and not equivalent if they belong to different classes. Moreover, we give a similar classification for operational quantities characterizing lower semi-Fredholm operators.
Słowa kluczowe
Czasopismo
Rocznik
Tom
114
Numer
1
Strony
13-27
Opis fizyczny
Daty
wydano
1995
otrzymano
1993-07-16
poprawiono
1995-01-05
Twórcy
  • Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife), Spain
Bibliografia
  • [1] D. E. Edmunds and W. D. Evans, Spectral Theory and Differential Operators, Clarendon Press, Oxford, 1986.
  • [2] A. S. Faĭnshteĭn, Measures of noncompactness of linear operators and analogues of the minimum modulus for semi-Fredholm operators, in: Spectral Theory of Operators and its Applications, No. 6, "Èlm", Baku, 1985, 182-195 (in Russian); MR 87k:47025; Zbl. 634#47010.
  • [3] K.-H. Förster and E.-O. Liebetrau, Semi-Fredholm operators and sequence conditions, Manuscripta Math. 44 (1983), 35-44.
  • [4] S. Goldberg, Unbounded Linear Operators, McGraw-Hill, New York, 1966.
  • [5] M. González and A. Martinón, Operational quantities derived from the norm and measures of noncompactness, Proc. Roy. Irish Acad. Sect. A 91 (1991), 63-70.
  • [5] M. González and A. Martinón, Fredholm theory and space ideals, Boll. Un. Mat. Ital. B (7) 7 (1993), 473-488.
  • [7] R. C. James, Uniformly nonsquare Banach spaces, Ann. of Math. 80 (1964), 542-550.
  • [8] A. Lebow and M. Schechter, Semigroups of operators and measures of noncompactness, J. Funct. Anal. 7 (1971), 1-26.
  • [9] A. Martinón, Cantidades operacionales en teoría de Fredholm, thesis, Univ. La Laguna, 1989.
  • [10] E. Odell and T. Schlumprecht, The distortion problem, Acta Math. 173 (1994), 259-281.
  • [11] A. Pietsch, Operator Ideals, North-Holland, Amsterdam, 1980.
  • [12] V. Rakočević, Measures of non-strict-singularity of operators, Mat. Vesnik 35 (1983), 79-82.
  • [13] M. Schechter, Quantities related to strictly singular operators, Indiana Univ. Math. J. 21 (1972), 1061-1071.
  • [14] M. Schechter and R. Whitley, Best Fredholm perturbation theorems, Studia Math. 90 (1988), 175-190.
  • [15] T. Schlumprecht, An arbitrarily distortable Banach space, Israel J. Math. 76 (1991), 81-95.
  • [16] A. A. Sedaev, The structure of certain linear operators, Mat. Issled. 5 (1970), 166-175 (in Russian); MR 43#2540; Zbl. 247#47005.
  • [17] H.-O. Tylli, On the asymptotic behaviour of some quantities related to semi-Fredholm operators, J. London Math. Soc. (2) 31 (1985), 340-348.
  • [18] L. Weis, Über strikt singuläre und strikt cosinguläre Operatoren in Banachräumen, dissertation, Univ. Bonn, 1974.
  • [19] J. Zemánek, Geometric characteristics of semi-Fredholm operators and their asymptotic behaviour, Studia Math. 80 (1984), 219-234.
  • [20] J. Zemánek, The semi-Fredholm radius of a linear operator, Bull. Polish Acad. Sci. Math. 32 (1984), 67-76.
  • [21] J. Zemánek, On the Δ-characteristic of M. Schechter, in: Proc. Second Internat. Conf. on Operator Algebras, Ideals and Their Applications in Theoretical Physics, Teubner-Texte Math. 67, Teubner, Leipzig, 1984, 232-234.
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Bibliografia
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