  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
codi-mension of subspaces. To realize this aim, the main idea is the
introduction of new recursive assumptions and useful consequences of the Baire
category theorem and of the Banach isomorphism theorem.
