P-adic Spaces of Continuous Functions II

Katsaras, Athanasios

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 ${\aleph }_o$-barrelled, polarly ${\ell }^{\infty }$-barrelled or polarly $c_o$-barrelled. Also, tensor products of spaces of continuous functions as well as tensor products of certain $E^{\prime }$-valued measures are investigated.

Classification : 46S10, 46G10
Mots clés : Non-Archimedean fields, zero-dimensional spaces, locally convex spaces

[1] Aguayo, J.; Katsaras, A. K.; Navarro, S. On the dual space for the strict topology ${\beta }_1$ and the space $M\left(X\right)$ in function space, Ultrametric functional analysis (Contemp. Math.), Volume 384, Amer. Math. Soc., Providence, RI, 2005, pp. 15-37 | MR | Zbl

[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 | Zbl

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

[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 | DOI | MR | Zbl

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