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Regularity in \(p\)-adic inductive limits. (English) Zbl 1135.46044

This is a survey paper on the most important results on \(p\)-adic inductive limits obtained in the last years, mainly by the authors. Some new results are included as well as, for instance, a \(p\)-adic version of the Dieudonné-Schwartz theorem, stating that every strict LF-limit is regular. An LF-limit \(E\) of subspaces spaces \(E_1\subset E_2\subset\dots\) is called regular if every bounded subset of \(E\) is contained in some \(E_n.\) The topics covered in this survey are: strictness and closedness properties, regularity properties, the \(p\)-adic Dieudonné-Schwartz theorem. The paper ends with a set of useful examples.

MSC:

46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
46A13 Spaces defined by inductive or projective limits (LB, LF, etc.)
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Full Text: Euclid