Nonarchimedean Functional Analysis

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Duality for admissible locally analytic representations (2004, background): “ Can c (G,K) is of compact type by [ST1] Prop. 1.2(ii). In this situation [ST1] Cor. 3.3 says that both D(G,K)-actions on DK(G) are separately continuous. If H⊆ Gis any compact open subgroup then, by [NFA] 9.10, we have DK(G) = Y g∈G/H D(gH,K) . The projection map ℓG,H : DK(G) −→ D(H,K) onto the fac”
Finiteness of rigid cohomology with coefficients (2002, methodology): “3 Review of p-adic functional analysis To make more progress, we need some basic facts from p-adic functional analysis; we state the relevant results here and refer to [Cr] (or [Sc]) for further discussion.”
On fields of totally $\mathfrak{S}$-adic numbers. With an appendix by Florian Pop (2012, result): “In a spherically complete space, many of the classical results of functional analysis hold, as the Hahn-Banach, Banach-Steinhaus and Open Mapping Theorems [Sch02].”