Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A Theorem of the Alternative in Banach Lattices

Author: Jean B. Lasserre
Journal: Proc. Amer. Math. Soc. 126 (1998), 189-194
MSC (1991): Primary 47A50, 46B42, 46H10
MathSciNet review: 1452808
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. Robert B. Ash, Real analysis and probability, Academic Press, New York-London, 1972. Probability and Mathematical Statistics, No. 11. MR 0435320
  • 2. 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
  • 3. B. D. Craven and J. J. Koliha, Generalizations of Farkas’ theorem, SIAM J. Math. Anal. 8 (1977), no. 6, 983–997. MR 0471302,
  • 4. Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers, Ltd., London, 1958. MR 0117523
  • 5. J.B. Lasserre, A Farkas Lemma without a standard closure condition, SIAM J. Contr. Optim. 35 (1997), 265-272. CMP 97:07
  • 6. 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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47A50, 46B42, 46H10

Retrieve articles in all journals with MSC (1991): 47A50, 46B42, 46H10

Additional Information

Jean B. Lasserre
Affiliation: LAAS-CNRS, 7 Av. du Colonel Roche, 31077 Toulouse Cédex, France

Keywords: Linear systems in Banach spaces, Farkas lemma, Banach lattices
Received by editor(s): July 8, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society