On irreducible representations of compact $p$-adic analytic groups

We prove that the canonical dimension of a coadmissible representation of a
semisimple $p$-adic Lie group in a $p$-adic Banach space is either zero or at
least half the dimension of a non-zero coadjoint orbit. To do this we establish
analogues for $p$-adically completed enveloping algebras of Bernstein's
inequality for modules over Weyl algebras, the Beilinson-Bernstein localisation
theorem and Quillen's Lemma about the endomorphism ring of a simple module over
an enveloping algebra.