  We establish duality theory of p-adic unitary Banach representations of
locally profinite groups. This is an extension of Iwasawa theory for profinite
groups by P. Schneider and J. Teitelbaum. We also establish a criterion for an
irreducibility of a unitary representation by certain simpleness of the Iwasawa
module dual to it. Through the duality, the continuous induction of a unitary
Banach representation of a closed subgroup is interpreted as a certain
induction of Iwasawa module. It gives an explicit description of the dual of a
continuous parabolic induction on GL_n(Q_p).
