Bounded subsets of non-Archimedean Banach spaces and of their rings of continuous operators
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (1982), pp. 39-43
Voir la notice de l'article provenant de la source Math-Net.Ru
The purpose of the present paper is to prove the mutual equivalence of some boundedness properties of subsets of non-archimedean (n. a.) Banach spaces. In particular, the boundedness by norm is equivalent to the weak boundedness by functional. We consider some properties of bounded subsets of n. a. vector spaces and their operator rings. For example, we give an algebraic characterization of bounded subsets in the operator rings of n. a. vector spaces and, as a corollary, we obtain an axiomatic description of the operator norm.
@article{VMUMM_1982_5_a10,
author = {L. I. Mikhaleva},
title = {Bounded subsets of {non-Archimedean} {Banach} spaces and of their rings of continuous operators},
journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
pages = {39--43},
publisher = {mathdoc},
number = {5},
year = {1982},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMUMM_1982_5_a10/}
}
TY - JOUR AU - L. I. Mikhaleva TI - Bounded subsets of non-Archimedean Banach spaces and of their rings of continuous operators JO - Vestnik Moskovskogo universiteta. Matematika, mehanika PY - 1982 SP - 39 EP - 43 IS - 5 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VMUMM_1982_5_a10/ LA - ru ID - VMUMM_1982_5_a10 ER -
%0 Journal Article %A L. I. Mikhaleva %T Bounded subsets of non-Archimedean Banach spaces and of their rings of continuous operators %J Vestnik Moskovskogo universiteta. Matematika, mehanika %D 1982 %P 39-43 %N 5 %I mathdoc %U http://geodesic.mathdoc.fr/item/VMUMM_1982_5_a10/ %G ru %F VMUMM_1982_5_a10
L. I. Mikhaleva. Bounded subsets of non-Archimedean Banach spaces and of their rings of continuous operators. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (1982), pp. 39-43. http://geodesic.mathdoc.fr/item/VMUMM_1982_5_a10/