Universal norms of partially de Rham $B$-pairs and perfectness in Lubin--Tate Iwasawa theory

We study the behaviour of partially de Rham Selmer groups of $B$-pairs along abelian $p$-adic Lie extensions. In the cyclotomic case we compare them with the universal norms studied by Berger. For analytic Lubin–Tate $(\phi ,\mathrm{\Gamma })$-modules we prove that the $\mathrm{\Psi }=1$ eigenspace is coadmissible of the expected rank over the algebra of analytic distributions and establish a comparison result between its Lie-algebra coinvariants and the projective limit of the partially de Rham Selmer groups of the attached $B$-pair.