Abstract

This paper presents necessary and sufficient conditions for the existence of solutions to cone-constrained linear equations in some function spaces. These conditions yield, in particular, the classical Fredholm alternative for compact operators. We use a formulation that under some conditions permits to apply the Generalized Farkas Theorem of Craven and Koliha. The Poissson Equation for stochastic (Markov) kernels, the Volterra and Fredholm equations for non-compact operators in Lₚ spaces, are among the particular cases of potential application.

Author information

Contact details are reproduced from the original publication and may be historical.

O. Hernandez-Lerma

Departamento de Matemáticas, CINVESTAV-IPN, A. Postal 14-740, México D.F. 07000, Mexico.

J. B. Lasserre

LAAS-CNRS, 7 Avenue du Colonel Roche, 31077 Toulouse Cédex, France.

Keywords

  • Linear equations in Banach spaces
  • Generalized Farkas Theorem
  • Fredholm alternative

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Suggested citation

O. Hernandez-Lerma, J. B. Lasserre. “Cone-Constrained Linear Equations in Banach Spaces.” Journal of Convex Analysis 4 (1997), No. 1, 149–164. https://doi.org/10.68381/jca04007

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Published by Heldermann Verlag, 1997. Rights now held by Banach Press LLC.