Abstract: Let L be a finite extension of Qp, and let K
be a spherically complete non-archimedean extension field of L.
In this paper we introduce a restricted category of continuous
representations of locally L-analytic groups G in locally
convex K-vector spaces.
We call the objects of
this category "admissible" representations and we establish some
of their basic properties. Most importantly we show that (at least
when G is compact) the category of admissible representations in
our sense can be algebraized; it is faithfully full
(anti)-embedded into the category of modules over the locally
analytic distribution algebra D(G,K) of G over K.
As an application of our theory, we prove the topological
irreducibility of generic members of the p-adic principal series
Peter Schneider and Jeremy Teitelbaum <email@example.com, firstname.lastname@example.org>