Weak bases in p -adic spaces

N. De Grande-De Kimpe; J. Kąkol; C. Perez-Garcia; W. H. Schikhof

Bollettino dell'Unione Matematica Italiana (2002)

  • Volume: 5-B, Issue: 3, page 667-676
  • ISSN: 0392-4041

Abstract

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We study polar locally convex spaces over a non-archimedean non-trivially valued complete field with a weak topological basis. We prove two completeness theorems and a Hahn-Banach type theorem for locally convex spaces with a weak Schauder basis.

How to cite

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De Grande-De Kimpe, N., et al. "Weak bases in $p$-adic spaces." Bollettino dell'Unione Matematica Italiana 5-B.3 (2002): 667-676. <http://eudml.org/doc/195070>.

@article{DeGrande2002,
abstract = {We study polar locally convex spaces over a non-archimedean non-trivially valued complete field with a weak topological basis. We prove two completeness theorems and a Hahn-Banach type theorem for locally convex spaces with a weak Schauder basis.},
author = {De Grande-De Kimpe, N., Kąkol, J., Perez-Garcia, C., Schikhof, W. H.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {667-676},
publisher = {Unione Matematica Italiana},
title = {Weak bases in $p$-adic spaces},
url = {http://eudml.org/doc/195070},
volume = {5-B},
year = {2002},
}

TY - JOUR
AU - De Grande-De Kimpe, N.
AU - Kąkol, J.
AU - Perez-Garcia, C.
AU - Schikhof, W. H.
TI - Weak bases in $p$-adic spaces
JO - Bollettino dell'Unione Matematica Italiana
DA - 2002/10//
PB - Unione Matematica Italiana
VL - 5-B
IS - 3
SP - 667
EP - 676
AB - We study polar locally convex spaces over a non-archimedean non-trivially valued complete field with a weak topological basis. We prove two completeness theorems and a Hahn-Banach type theorem for locally convex spaces with a weak Schauder basis.
LA - eng
UR - http://eudml.org/doc/195070
ER -

References

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  1. DE GRANDE-DE KIMPE, N., On the structure of locally K -convex spaces with a Schauder base, Indag. Math., 34 (1972), 396-406. Zbl0244.46005MR320689
  2. DE GRANDE-DE KIMPE, N.- PEREZ-GARCIA, C., Weakly closed subspaces and the Hahn-Banach extension property in p -adic analysis, Indag. Math., 91 (1988), 253-261. Zbl0678.46055MR964832
  3. DE GRANDE DE KIMPE, N.- KĄKOL, J.- PEREZ GARCIA, C., SCHIKHOF, W. H., Orthogonal sequences in non-archimedean locally convex spaces, Indag. Math. N.S., 11 (2000), 187-195. Zbl0980.46056MR1813159
  4. DIEROLF, S., The barrelled space associated with a bornological space need not be bornological, Bull. London Math. Soc., 12 (1980), 60-62. Zbl0402.46002MR565486
  5. GILSDORF, T.- KĄKOL, J., On some non-archimedean closed graph theorems, In: Proc 4th Intern. Conf. on p -adic Functional Analysis, Nijmegen, The Netherlands, Marcel Dekker, 192 (1997), 153-159. Zbl0889.46064MR1459210
  6. KALTON, N. J., Schauder decomposition and completeness, Bull. London Math. Soc., 2 (1970), 34-36. Zbl0196.13601MR259547
  7. KAMTHAN, P. K.- GUPTA, M., Weak Schauder bases and completeness, Proc. Roy. Irish Ac., 78 (1978), 51-54. Zbl0388.46002MR506956
  8. KĄKOL, J., The weak basis theorem for K -Banach spaces, Bull. Soc. Math. Belg., 45 (1993), 1-4. Zbl0728.46003MR1314928
  9. KĄKOL, J.- GILSDORF, T., On the weak basis theorems for p -adic locally convex spaces, In: Proc. 5th Intern. Conf. on p -adic Functional Analysis, Poznań, Poland, Marcel Dekker, 207 (1999), 149-167. Zbl0949.46039MR1702053
  10. PEREZ-GARCIA, C.- SCHIKHOF, W. H., p -Adic barrelledness and spaces of countable type, Indian J. Pure Appl. Math., 29 (1998), 1099-1109. Zbl0926.46067MR1658689
  11. PEREZ-GARCIA, C.- SCHIKHOF, W. H., The Orlicz-Pettis property in p -adic analysis, Collect. Math., 43 (1992), 225-233. Zbl0788.46078MR1252732
  12. VAN ROOIJ, A. C. M., Non-archimedean functional analysis, Marcel Dekker, New York (1978). Zbl0396.46061MR512894
  13. SCHIKHOF, W. H., Locally convex spaces over nonspherically complete valued fields, Bull. Soc. Math. Belg., 38 (1986), 187-224. Zbl0615.46071MR871313
  14. ŚLIWA, W., Every infinite-dimensional non-archimedean Fréchet space has an orthogonal basic sequence (to appear in Indag. Math.). Zbl0980.46057
  15. VAN TIEL, J., Espaces localement K -convexes, Indag. Math, 27 (1965), 249-289. Zbl0133.06502MR179593
  16. WEBB, J. H., Schauder decompositions in locally convex spaces, Camb. Phil. Soc., 76 (1974), 145-152. Zbl0283.46003MR350370

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