Generating real maps on a biordered set

Antonio Martinón

Commentationes Mathematicae Universitatis Carolinae (1991)

  • Volume: 32, Issue: 2, page 265-272
  • ISSN: 0010-2628

Abstract

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Several authors have defined operational quantities derived from the norm of an operator between Banach spaces. This situation is generalized in this paper and we present a general framework in which we derivate several maps X → ℝ from an initial one X → ℝ , where X is a set endowed with two orders, ≤ and ≤ * , related by certain conditions. We obtain only three different derivated maps, if the initial map is bounded and monotone.

How to cite

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Martinón, Antonio. "Generating real maps on a biordered set." Commentationes Mathematicae Universitatis Carolinae 32.2 (1991): 265-272. <http://eudml.org/doc/247279>.

@article{Martinón1991,
abstract = {Several authors have defined operational quantities derived from the norm of an operator between Banach spaces. This situation is generalized in this paper and we present a general framework in which we derivate several maps $X\rightarrow \mathbb \{R\}$ from an initial one $X\rightarrow \mathbb \{R\}$, where $X$ is a set endowed with two orders, $\le $ and $\le ^\{\ast \}$, related by certain conditions. We obtain only three different derivated maps, if the initial map is bounded and monotone.},
author = {Martinón, Antonio},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {derivated map; biordered set; admissible order; infimum of the operator norms; upper semi-Fredholm operators; biordered space},
language = {eng},
number = {2},
pages = {265-272},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Generating real maps on a biordered set},
url = {http://eudml.org/doc/247279},
volume = {32},
year = {1991},
}

TY - JOUR
AU - Martinón, Antonio
TI - Generating real maps on a biordered set
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1991
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 32
IS - 2
SP - 265
EP - 272
AB - Several authors have defined operational quantities derived from the norm of an operator between Banach spaces. This situation is generalized in this paper and we present a general framework in which we derivate several maps $X\rightarrow \mathbb {R}$ from an initial one $X\rightarrow \mathbb {R}$, where $X$ is a set endowed with two orders, $\le $ and $\le ^{\ast }$, related by certain conditions. We obtain only three different derivated maps, if the initial map is bounded and monotone.
LA - eng
KW - derivated map; biordered set; admissible order; infimum of the operator norms; upper semi-Fredholm operators; biordered space
UR - http://eudml.org/doc/247279
ER -

References

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  1. Banas J., Goebel K., Measures of Noncompactness in Banach Spaces, Marcel Dekker, Lecture Notes in Pure and Applied Math., vol.60; New York, Basel, 1980. Zbl0441.47056MR0591679
  2. Bourbaki N., Éléments de Mathématique. Topologie Générale, Hermann, Paris, 1971. Zbl1107.54001MR0358652
  3. Fajnshtejn A.S., On measures of noncompactness of linear operators and analogs of the minimal modulus for semi-Fredholm operators (in Russian), Spektr. Teor. Oper. 6 (1985), 182-195 Zbl 634 #47010. (1985) 
  4. Gonzalez M., Martinon A., Operational quantities and operator ideals, Actas XIV Jornadas Hispano-Lusas Mat. (1989), Univ. La Laguna, vol. I, 1990, 383-387. MR1112904
  5. Gonzalez M., Martinon A., Operational quantities derived from the norm and measures of noncompactness, Proc. Royal Irish Acad., to appear. MR1173159
  6. Gonzalez M., Martinon A., A generalization of semi-Fredholm operators, 1990, preprint. 
  7. Lebow A., Schechter M., Semigroups of operators and measures of noncompactness, J. Func. Anal. 7 (1971), 1-26. (1971) Zbl0209.45002MR0273422
  8. Martinon A., Generating operational quantities in Fredholm theory, Actas XIV Jornadas Hispano-Lusas Mat. (1989), Univ. La Laguna, vol. I, 1990, 449-453. MR1112916
  9. Martinon A., Cantidades operacionales en Teoría de Fredholm (Tesis), Univ. La Laguna, 1989. MR1067932
  10. Pietsch A., Operator Ideals, North-Holland; Amsterdam, New York, Oxford, 1980. Zbl1012.47001MR0582655
  11. Schechter M., Quantities related to strictly singular operators, Indiana Univ. Math. J. 21 (1972), 1061-1071. (1972) Zbl0274.47007MR0295103
  12. Sedaev A.A., The structure of certain linear operators (in Russian), Mat. Issled. 5 (1970), 166-175 MR 43 #2540; Zbl. 247 #47005. (1970) MR0276800
  13. Tylli H.-O., On the asymptotic behaviour of some quantities related to semi-Fredholm operators, J. London Math. Soc. (2) 31 (1985), 340-348. (1985) Zbl0582.47004MR0809955
  14. Weis L., Über strikt singulare und strikt cosingulare Operatoren in Banachräumen (Dissertation), Univ. Bonn, 1974. 
  15. Zemanek J., Geometric characteristics of semi-Fredholm operators and their asymptotic behaviour, Studia Math. 80 (1984), 219-234. (1984) Zbl0556.47008MR0783991

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