# P-adic Spaces of Continuous Functions II

Athanasios Katsaras^{[1]}

- [1] Department of Mathematics University of Ioannina Ioannina, 45110 Greece

Annales mathématiques Blaise Pascal (2008)

- Volume: 15, Issue: 2, page 169-188
- ISSN: 1259-1734

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topKatsaras, Athanasios. "P-adic Spaces of Continuous Functions II." Annales mathématiques Blaise Pascal 15.2 (2008): 169-188. <http://eudml.org/doc/10559>.

@article{Katsaras2008,

abstract = {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.},

affiliation = {Department of Mathematics University of Ioannina Ioannina, 45110 Greece},

author = {Katsaras, Athanasios},

journal = {Annales mathématiques Blaise Pascal},

keywords = {Non-Archimedean fields; zero-dimensional spaces; locally convex spaces; non-archimedean fields; locally convex spaces of continuous functions},

language = {eng},

month = {7},

number = {2},

pages = {169-188},

publisher = {Annales mathématiques Blaise Pascal},

title = {P-adic Spaces of Continuous Functions II},

url = {http://eudml.org/doc/10559},

volume = {15},

year = {2008},

}

TY - JOUR

AU - Katsaras, Athanasios

TI - P-adic Spaces of Continuous Functions II

JO - Annales mathématiques Blaise Pascal

DA - 2008/7//

PB - Annales mathématiques Blaise Pascal

VL - 15

IS - 2

SP - 169

EP - 188

AB - 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.

LA - eng

KW - Non-Archimedean fields; zero-dimensional spaces; locally convex spaces; non-archimedean fields; locally convex spaces of continuous functions

UR - http://eudml.org/doc/10559

ER -

## References

top- J. Aguayo, A. K. Katsaras, S. Navarro, On the dual space for the strict topology ${\beta}_{1}$ and the space $M\left(X\right)$ in function space, Ultrametric functional analysis 384 (2005), 15-37, Amer. Math. Soc., Providence, RI Zbl1104.46046MR2174775
- A. K. Katsaras, On the strict topology in non-Archimedean spaces of continuous functions, Glas. Mat. Ser. III 35(55) (2000), 283-305 Zbl0970.46049MR1812558
- A. K. Katsaras, P-adic Spaces of continuous functions I, Ann. Math. Blaise Pascal 15 (2008), 109-133 Zbl1158.46050MR2418016
- A. K. Katsaras, A. Beloyiannis, Tensor products of non-Archimedean weighted spaces of continuous functions, Georgian Math. J. 6 (1999), 33-44 Zbl0921.46085MR1672990
- A. C. M. van Rooij, Non-Archimedean functional analysis, 51 (1978), Marcel Dekker Inc., New York Zbl0396.46061MR512894

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