Download PDF - Operational quantities characterizing semi-Fredholm operatorsAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Operational quantities characterizing semi-Fredholm operators

Authors 1, 2

Affiliations

  1. Departamento de Matemáticas, Universidad de Cantabria, 39071 Santander, Spain
  2. Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife), Spain

Abstract

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.

Keywords

ENG
operational quantity, semi-Fredholm operator

Bibliography

  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.
  6. 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.
Studia Mathematica
1995/114/1
Export to PBN, Opens in new tab
Pages:
13-27
Main language of publication
English
Received
1993-07-16
Accepted
1995-01-05
Published
1995
Exact and natural sciences