A theorem of the alternative in Banach lattices
HTML articles powered by AMS MathViewer
- by Jean B. Lasserre PDF
- Proc. Amer. Math. Soc. 126 (1998), 189-194 Request permission
Abstract:
We consider a linear sytem in a Banach lattice and provide a simple theorem of the alternative (or Farkas lemma) without the usual closure condition.References
- Robert B. Ash, Real analysis and probability, Probability and Mathematical Statistics, No. 11, Academic Press, New York-London, 1972. MR 0435320
- Haïm Brezis, Analyse fonctionnelle, Collection Mathématiques Appliquées pour la Maîtrise. [Collection of Applied Mathematics for the Master’s Degree], Masson, Paris, 1983 (French). Théorie et applications. [Theory and applications]. MR 697382
- B. D. Craven and J. J. Koliha, Generalizations of Farkas’ theorem, SIAM J. Math. Anal. 8 (1977), no. 6, 983–997. MR 471302, DOI 10.1137/0508076
- Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 0117523
- J.B. Lasserre, A Farkas Lemma without a standard closure condition, SIAM J. Contr. Optim. 35 (1997), 265–272.
- Kôsaku Yosida, Functional analysis, 6th ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 123, Springer-Verlag, Berlin-New York, 1980. MR 617913
Additional Information
- Jean B. Lasserre
- Affiliation: LAAS-CNRS, 7 Av. du Colonel Roche, 31077 Toulouse Cédex, France
- MR Author ID: 110545
- Email: lasserre@laas.fr
- Received by editor(s): July 8, 1996
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 189-194
- MSC (1991): Primary 47A50, 46B42, 46H10
- DOI: https://doi.org/10.1090/S0002-9939-98-04389-5
- MathSciNet review: 1452808