Summable families in topological vector spaces.

Michel Mazan

Revista Matemática Hispanoamericana (1982)

  • Volume: 42, Issue: 4-5-6, page 179-186
  • ISSN: 0373-0999

Abstract

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Let E and F be two vector spaces in separating duality. Let us consider T0, the uniform convergence topology on E on the partial sums of families of F which are weakly summable to 0 in F; then, if (E',T'0) is the completion of (E,T0), the finest locally convex topology T on F for which all the weakly summable families in F are also T-summable, is the uniform convergence topology on the T'0-compact subsets of E'. If F is a Banach space and E its dual space F', every weakly summable family in F is summable in F if and only if the closed unit ball of F' is a T0-compact set. If TZ is further the uniform convergence topology on F on the partial sums of absolutely summable and Ts(F)-summable to 0 sequences of F', F is reflexive if and only if F is Tz-complete. We give also in appendix a generalization of the Orlicz-Pettis theorem.

How to cite

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Mazan, Michel. "Familles sommables dans les espaces vectoriels topologiques.." Revista Matemática Hispanoamericana 42.4-5-6 (1982): 179-186. <http://eudml.org/doc/39810>.

@article{Mazan1982,
author = {Mazan, Michel},
journal = {Revista Matemática Hispanoamericana},
keywords = {Espacios vectoriales topológicos; Convergencia; Familias sumables; vector spaces in separating duality; weakly summable family; reflexive; Orlicz-Pettis theorem},
language = {fre},
number = {4-5-6},
pages = {179-186},
title = {Familles sommables dans les espaces vectoriels topologiques.},
url = {http://eudml.org/doc/39810},
volume = {42},
year = {1982},
}

TY - JOUR
AU - Mazan, Michel
TI - Familles sommables dans les espaces vectoriels topologiques.
JO - Revista Matemática Hispanoamericana
PY - 1982
VL - 42
IS - 4-5-6
SP - 179
EP - 186
LA - fre
KW - Espacios vectoriales topológicos; Convergencia; Familias sumables; vector spaces in separating duality; weakly summable family; reflexive; Orlicz-Pettis theorem
UR - http://eudml.org/doc/39810
ER -

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