Discrete time Pontryagin principles in Banach spaces.
Résumé
The aim of this paper is to establish Pontryagin's principles in a dicrete-time infinite-horizon setting when the state variables and the control variables belong to infinite-dimensional Banach spaces. In comparison with previous results on this question, we delete conditions of finiteness of codimension of subspaces. To realize this aim, the main ideas are the introduction of new recursive assumptions and useful consequences of the Baire category theorem and of the Banach isomorphism theorem.