P-adic Spaces of Continuous Functions II
Annales Mathématiques Blaise Pascal, Tome 15 (2008) no. 2, pp. 169-188.

Necessary and sufficient conditions are given so that the space C(X,E) of all continuous functions from a zero-dimensional topological space X to a non-Archimedean locally convex space E, equipped with the topology of uniform convergence on the compact subsets of X, to be polarly absolutely quasi-barrelled, polarly o -barrelled, polarly -barrelled or polarly c o -barrelled. Also, tensor products of spaces of continuous functions as well as tensor products of certain E -valued measures are investigated.

DOI : https://doi.org/10.5802/ambp.246
Classification : 46S10,  46G10
Mots clés : Non-Archimedean fields, zero-dimensional spaces, locally convex spaces
@article{AMBP_2008__15_2_169_0,
     author = {Katsaras, Athanasios},
     title = {P-adic Spaces of Continuous Functions II},
     journal = {Annales Math\'ematiques Blaise Pascal},
     pages = {169--188},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {15},
     number = {2},
     year = {2008},
     doi = {10.5802/ambp.246},
     mrnumber = {2468042},
     zbl = {1166.46042},
     language = {en},
     url = {www.numdam.org/item/AMBP_2008__15_2_169_0/}
}
Katsaras, Athanasios. P-adic Spaces of Continuous Functions II. Annales Mathématiques Blaise Pascal, Tome 15 (2008) no. 2, pp. 169-188. doi : 10.5802/ambp.246. http://www.numdam.org/item/AMBP_2008__15_2_169_0/

[1] Aguayo, J.; Katsaras, A. K.; Navarro, S. On the dual space for the strict topology β 1 and the space M(X) in function space, Ultrametric functional analysis (Contemp. Math.) Volume 384, Amer. Math. Soc., Providence, RI, 2005, pp. 15-37 | MR 2174775 | Zbl 1104.46046

[2] Katsaras, A. K. On the strict topology in non-Archimedean spaces of continuous functions, Glas. Mat. Ser. III, Volume 35(55) (2000) no. 2, pp. 283-305 | MR 1812558 | Zbl 0970.46049

[3] Katsaras, A. K. P-adic Spaces of continuous functions I, Ann. Math. Blaise Pascal, Volume 15 (2008) no. 1, pp. 109-133 | Article | Numdam | MR 2418016 | Zbl pre05312018

[4] Katsaras, A. K.; Beloyiannis, A. Tensor products of non-Archimedean weighted spaces of continuous functions, Georgian Math. J., Volume 6 (1999) no. 1, pp. 33-44 | Article | MR 1672990 | Zbl 0921.46085

[5] van Rooij, A. C. M. Non-Archimedean functional analysis, Monographs and Textbooks in Pure and Applied Math., Volume 51, Marcel Dekker Inc., New York, 1978 | MR 512894 | Zbl 0396.46061