Non-archimedean Eberlein-Šmulian theory
Summary: It is shown that, for a large class of non-Archimedean normed spaces \(E\), a subset \(X\) is weakly compact as soon as \(f(X)\) is compact for all \(f\in E'\), a fact that has no analogue in functional analysis over the real or complex numbers. As a corollary, we derive a non-Archimedean version of the Eberlein-Šmulian Theorem.
scientific article; zbMATH DE number 930039
scientific article