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Let E and F be two vector spaces in separating duality. Let us consider T, 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') is the completion of (E,T), 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'-compact subsets of E'. If F is a Banach space and E its dual space F', every weakly summable family in F is summable...
Soit I un ensembre quelconque. Si M est un sous-module quelconque de A et N un sous-module de M, α-dual de M (Mazan 1976), le dual topologique de M, muni de la topologie faible, T(N), est, sous certaines conditions, isomorphe topologiquement à N/M. Ce résultat peut s'étendre au cas où M et N sont deux modules quelconques en dualité. Cette note étudie aussi les topologies T de M, compatibles avec la dualité et introduit la notion de topologie uniforme.
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