  We introduce a sheaf of infinite order differential operators D-cap on smooth
rigid analytic spaces that is a rigid analytic quantisation of the cotangent
bundle. We show that the sections of this sheaf over sufficiently small
affinoid varieties are Fr\'echet-Stein algebras, and use this to define
co-admissible sheaves of D-cap-modules. We prove analogues of Cartan's Theorems
A and B for co-admissible D-cap-modules.
