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 from an initial one X , 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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  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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