×
Schikhof, W. H.

Minimal-Hausdorff \(p\)-adic locally convex spaces. (English) Zbl 0828.46068

Ann. Math. Blaise Pascal 2, No. 1, 259-266 (1995).
Summary: We characterize, in various ways, those Hausdorff locally convex spaces over a non-archimedean valued field \(K\) that do not admit a strictly weaker Hausdorff locally convex topology. Our results extend the ones obtained by N. De Grande-De Kimpe in [Indag. Math. 33, 176-180 (1971; Zbl 0209.144)], for spherically complete \(K\). For an analogous theory for compactoids instead of locally convex spaces we refer to 2nd Conf. on \(p\)-adic Functional Analysis, Santiago de Chile (1992).

Cited in 7 Documents

MSC:

46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
46A03 General theory of locally convex spaces

Keywords:

Hausdorff locally convex spaces over a non-archimedean valued field; not admit a strictly weaker Hausdorff locally convex topology; compactoids

Citations:

Zbl 0209.144
PDF BibTeX XML Cite
\textit{W. H. Schikhof}, Ann. Math. Blaise Pascal 2, No. 1, 259--266 (1995; Zbl 0828.46068)
Full Text: DOI Numdam EuDML
  • logo of hbz
  • logo of WorldCat

References:

[1] De Grande-De Kimpe, N., c-compactness in locally K-convex spaces, Indag. Math.33 (1971), 176-180. · Zbl 0209.14404
[2] van Rooij, A.C.M., Non-Archimedean Functional Analysis. Marcel Dekker, New York (1978). · Zbl 0396.46061
[3] Schikhof, W.H., Locally convex spaces over non-spherically complete valued fields, Bull. Soc. Math. Belg.XXXVIII, serie B (1986), 187-224. · Zbl 0615.46071
[4] Schikhof, W.H., p-adic local compactoids, Report 8802, Department of Mathematics, Catholic University, Nijmegen, The Netherlands (1988). · Zbl 0712.46045
[5] Schikhof, W.H., More on duality between p-adic Banach spaces and compactoids, Report 9301, Department of Mathematics, Catholic University, Nijmegen, The Netherlands (1993).
[6] Schikhof, W.H., The equalization of p-adic Banach spaces and compactoids. To appear in the Proceedings of the Second International Conference on p-adic Functional Analysis, held in Santiago, Chile, 1992.
[7] van Tiel, J., Espaces localement K-convexes. Indag. Math.27 (1965), 249-289. · Zbl 0133.06502
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.