Operational quantities characterizing semi-Fredholm operators
Manuel González; Antonio Martinón
Studia Mathematica (1995)
- Volume: 114, Issue: 1, page 13-27
- ISSN: 0039-3223
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topGonzález, Manuel, and Martinón, Antonio. "Operational quantities characterizing semi-Fredholm operators." Studia Mathematica 114.1 (1995): 13-27. <http://eudml.org/doc/216176>.
@article{González1995,
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.},
author = {González, Manuel, Martinón, Antonio},
journal = {Studia Mathematica},
keywords = {operational quantity; semi-Fredholm operator; upper semi-Fredholm operators; lower semi-Fredholm operators},
language = {eng},
number = {1},
pages = {13-27},
title = {Operational quantities characterizing semi-Fredholm operators},
url = {http://eudml.org/doc/216176},
volume = {114},
year = {1995},
}
TY - JOUR
AU - González, Manuel
AU - Martinón, Antonio
TI - Operational quantities characterizing semi-Fredholm operators
JO - Studia Mathematica
PY - 1995
VL - 114
IS - 1
SP - 13
EP - 27
AB - 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.
LA - eng
KW - operational quantity; semi-Fredholm operator; upper semi-Fredholm operators; lower semi-Fredholm operators
UR - http://eudml.org/doc/216176
ER -
References
top- [1] D. E. Edmunds and W. D. Evans, Spectral Theory and Differential Operators, Clarendon Press, Oxford, 1986. Zbl0664.47014
- [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. Zbl0519.47009
- [4] S. Goldberg, Unbounded Linear Operators, McGraw-Hill, New York, 1966. Zbl0148.12501
- [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. Zbl0132.08902
- [8] A. Lebow and M. Schechter, Semigroups of operators and measures of noncompactness, J. Funct. Anal. 7 (1971), 1-26. Zbl0209.45002
- [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. Zbl0828.46005
- [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. Zbl0532.47006
- [13] M. Schechter, Quantities related to strictly singular operators, Indiana Univ. Math. J. 21 (1972), 1061-1071. Zbl0274.47007
- [14] M. Schechter and R. Whitley, Best Fredholm perturbation theorems, Studia Math. 90 (1988), 175-190. Zbl0611.47010
- [15] T. Schlumprecht, An arbitrarily distortable Banach space, Israel J. Math. 76 (1991), 81-95. Zbl0796.46007
- [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. Zbl0582.47004
- [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. Zbl0556.47008
- [20] J. Zemánek, The semi-Fredholm radius of a linear operator, Bull. Polish Acad. Sci. Math. 32 (1984), 67-76. Zbl0583.47016
- [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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