(Conférence n°3) Applications radonifiantes dans l'espace des séries convergentes
We show that the restriction operator of the space of holomorphic functions on a complex Lie group to an analytic subset V has a continuous linear right inverse if it is surjective and if V is a finite branched cover over a connected closed subgroup Γ of G. Moreover, we show that if Γ and G are complex Lie groups and V ⊂ Γ × G is an analytic set such that the canonical projection is finite and proper, then has a right inverse
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...