bdim: Biblioteca Digitale Italiana di Matematica

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Referenza completa

De Grande-De Kimpe, N. and Kąkol, J. and Perez-Garcia, C. and Schikhof, W. H.:
Weak bases in $p$-adic spaces
Bollettino dell'Unione Matematica Italiana Serie 8 5-B (2002), fasc. n.3, p. 667-676, Unione Matematica Italiana (English)
pdf (256 Kb), djvu (149 Kb). | MR1934373 | Zbl 1072.46051

Sunto

Si studiano spazi polari localmente convessi su un non trivialmente valutato campo completo non archimedeo con una debole base topologica. Dimostriamo due teoremi di completezza e un teorema tipo Hahn-Banach per spazi localmente convessi con una debole base di Schauder.
Referenze Bibliografiche
[1] N. DE GRANDE-DE KIMPE, On the structure of locally $K$-convex spaces with a Schauder base, Indag. Math., 34 (1972), 396-406. | MR 320689 | Zbl 0244.46005
[2] N. DE GRANDE-DE KIMPE-C. PEREZ-GARCIA, Weakly closed subspaces and the Hahn-Banach extension property in $p$-adic analysis, Indag. Math., 91 (1988), 253-261. | MR 964832 | Zbl 0678.46055
[3] N. DE GRANDE DE KIMPE-J. KĄKOL-C. PEREZ GARCIA, W. H. SCHIKHOF, Orthogonal sequences in non-archimedean locally convex spaces, Indag. Math. N.S., 11 (2000), 187-195. | MR 1813159 | Zbl 0980.46056
[4] S. DIEROLF, The barrelled space associated with a bornological space need not be bornological, Bull. London Math. Soc., 12 (1980), 60-62. | MR 565486 | Zbl 0402.46002
[5] T. GILSDORF-J. KĄKOL, On some non-archimedean closed graph theorems, In: Proc 4th Intern. Conf. on $p$p-adic Functional Analysis, Nijmegen, The Netherlands, Marcel Dekker, 192 (1997), 153-159. | MR 1459210 | Zbl 0889.46064
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[7] P. K. KAMTHAN-M. GUPTA, Weak Schauder bases and completeness, Proc. Roy. Irish Ac., 78 (1978), 51-54. | MR 506956 | Zbl 0388.46002
[8] J. KĄKOL, The weak basis theorem for $K$-Banach spaces, Bull. Soc. Math. Belg., 45 (1993), 1-4. | MR 1314928 | Zbl 0728.46003
[9] J. KĄKOL-T. GILSDORF, On the weak basis theorems for $p$-adic locally convex spaces, In: Proc. 5th Intern. Conf. on $p$p-adic Functional Analysis, Poznań, Poland, Marcel Dekker, 207 (1999), 149-167. | MR 1702053 | Zbl 0949.46039
[10] C. PEREZ-GARCIA-W. H. SCHIKHOF, $p$-Adic barrelledness and spaces of countable type, Indian J. Pure Appl. Math., 29 (1998), 1099-1109. | MR 1658689 | Zbl 0926.46067
[11] C. PEREZ-GARCIA-W. H. SCHIKHOF, The Orlicz-Pettis property in $p$-adic analysis, Collect. Math., 43 (1992), 225-233. | MR 1252732 | Zbl 0788.46078
[12] A. C. M. VAN ROOIJ, Non-archimedean functional analysis, Marcel Dekker, New York (1978). | MR 512894 | Zbl 0396.46061
[13] W. H. SCHIKHOF, Locally convex spaces over nonspherically complete valued fields, Bull. Soc. Math. Belg., 38 (1986), 187-224. | MR 871313 | Zbl 0615.46071
[14] W. ŚLIWA, Every infinite-dimensional non-archimedean Fréchet space has an orthogonal basic sequence (to appear in Indag. Math.). | Zbl 0980.46057
[15] J. VAN TIEL, Espaces localement $K$-convexes, Indag. Math, 27 (1965), 249-289. | MR 179593 | Zbl 0133.06502
[16] J. H. WEBB, Schauder decompositions in locally convex spaces, Camb. Phil. Soc., 76 (1974), 145-152. | MR 350370 | Zbl 0283.46003

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