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A Theorem of the Alternative in Banach Lattices
Author(s):
Jean
B.
Lasserre
Journal:
Proc. Amer. Math. Soc.
126
(1998),
189-194.
MSC (1991):
Primary 47A50, 46B42, 46H10
MathSciNet review:
1452808
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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:
- 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
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Additional Information:
Jean
B.
Lasserre
Affiliation:
LAAS-CNRS, 7 Av. du Colonel Roche, 31077 Toulouse Cédex, France
Email:
lasserre@laas.fr
DOI:
10.1090/S0002-9939-98-04389-5
PII:
S 0002-9939(98)04389-5
Keywords:
Linear systems in Banach spaces,
Farkas lemma,
Banach lattices
Received by editor(s):
July 8, 1996
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1998,
American Mathematical Society
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