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

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. R.B. Ash, Real Analysis and Probability, Academic Press, New York, 1972. MR 55:8280
  • 2. H. Brézis, Analyse Fonctionnelle, Masson, Paris, 1983 MR 85a:46001
  • 3. B.D. Craven and J.J. Koliha, Generalizations of Farkas' Theorem, SIAM J. Math. Anal. 8 (1977), 983-997. MR 57:11039
  • 4. N. Dunford, J.T. Schwartz, Linear Operators. Part I: General Theory, Interscience Publishers, Inc., New York, 1958. MR 22:8302
  • 5. J.B. Lasserre, A Farkas Lemma without a standard closure condition, SIAM J. Contr. Optim. 35 (1997), 265-272. CMP 97:07
  • 6. K. Yosida, Functional Analysis, 6th ed., Springer-Verlag, New York, 1980. MR 82i:46002

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

American Mathematical Society