Polar Topologies on sequence spaces in non-archimedean analysis
DOI:
https://doi.org/10.4067/S0716-09172012000200002Keywords:
Locally K-convex topologies, non archimedean sequence spaces, Schauder basis, separated duality, topologías localmente K-convexas, espacios secuenciales no arquimedeanos, base de Schauder, dualidad separada.Abstract
The purpose of the present paper is to develop a theory of a duality in sequence spaces over a non-archimedean vector space. We introduce polar topologies in such spaces, and we give basic results characterizing compact, C-compact, complete and AK —complete subsets related to these topologies.References
[1] R. Ameziane Hassani, M. Babahmed, Topologies polaires compatibles avec une dualite separante sur un corps value non-Archimedien, Proyecciones Vol. 20, Num. 2, pp. 217-240, (2001).
[2] H.R. Chillingworth, Generalised ”dual” sequence spaces, Ned. Akad. Proc. Ser. A. 61, pp. 307-515, (1958).
[3] A. El amrani, R. Ameziane Hassani and M. Babahmed, Topologies on sequence spaces in non-archimedean analysis, J. of Mathematical Sciences: Advances and Applications Vol. 6, Num. 2, pp. 193-214, (2010).
[4] T. Komura; Y. Komura, sur les espaces parfaits de suites et leurs generalisations, J. Math. Soc. Japon. 15, pp. 319-338, (1963).
[5] G. Kothe, Topological vector spaces, Springer-Verlag Berlin Heidlberg New york, (1969).
[6] G. Kothe, Neubegrundung der theorie der vollkommen Raume, Math. Nach. 4, pp. 70-80, (1951).
[7] G. Kothe; O. Toeplitz, Lineare Raume mit unendlich vielen Koordinaten und Ringe unendlicher Matrizen, J. reine angew. Math. 171, pp. 193-226, (1934).
[8] G. Matthews, Generalised Rings of infinite matrices, Ned. Akad. Wet. Proc. 61, pp. 298-306 (1958).
[9] A.F.Monna, Analyse non-archimedienne, Springer-Verlag Berlin New York Heidelberg (1970).
[10] H.H. Schaefer, Topological vector spaces, Springer-Verlag Berlin New york Heidlberg, (1971).
[11] W. H. Schikhof, Locally convex spaces over nonspherically complete valued field I, II. Bull. Soc. Math. Belg. S´ er. B. 38, pp. 187-224, (1986).
[12] J. Van Tiel, Espaces localement K-convexes I-III, Indag. Math. 27, pp. 249-289 (1965).
[2] H.R. Chillingworth, Generalised ”dual” sequence spaces, Ned. Akad. Proc. Ser. A. 61, pp. 307-515, (1958).
[3] A. El amrani, R. Ameziane Hassani and M. Babahmed, Topologies on sequence spaces in non-archimedean analysis, J. of Mathematical Sciences: Advances and Applications Vol. 6, Num. 2, pp. 193-214, (2010).
[4] T. Komura; Y. Komura, sur les espaces parfaits de suites et leurs generalisations, J. Math. Soc. Japon. 15, pp. 319-338, (1963).
[5] G. Kothe, Topological vector spaces, Springer-Verlag Berlin Heidlberg New york, (1969).
[6] G. Kothe, Neubegrundung der theorie der vollkommen Raume, Math. Nach. 4, pp. 70-80, (1951).
[7] G. Kothe; O. Toeplitz, Lineare Raume mit unendlich vielen Koordinaten und Ringe unendlicher Matrizen, J. reine angew. Math. 171, pp. 193-226, (1934).
[8] G. Matthews, Generalised Rings of infinite matrices, Ned. Akad. Wet. Proc. 61, pp. 298-306 (1958).
[9] A.F.Monna, Analyse non-archimedienne, Springer-Verlag Berlin New York Heidelberg (1970).
[10] H.H. Schaefer, Topological vector spaces, Springer-Verlag Berlin New york Heidlberg, (1971).
[11] W. H. Schikhof, Locally convex spaces over nonspherically complete valued field I, II. Bull. Soc. Math. Belg. S´ er. B. 38, pp. 187-224, (1986).
[12] J. Van Tiel, Espaces localement K-convexes I-III, Indag. Math. 27, pp. 249-289 (1965).
Published
2012-06-18
How to Cite
[1]
R. Ameziane, A. El Amrani, and M. Babahmed, “Polar Topologies on sequence spaces in non-archimedean analysis”, Proyecciones (Antofagasta, On line), vol. 31, no. 2, pp. 103-123, Jun. 2012.
Issue
Section
Artículos
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
