(Conférence n°2) Une propriété caractéristique des processus linéaires continus. Applications aux opérateurs -radonifiants
The following result is proved: Let denote a power series space of infinite or of finite type, and equip with its canonical fundamental system of norms, R ∈ 0,∞, 1 ≤ p < ∞. Then a tamely exact sequence (⁎) exists iff α is strongly stable, i.e. , and a linear-tamely exact sequence (*) exists iff α is uniformly stable, i.e. there is A such that for all K. This result extends a theorem of Vogt and Wagner which states that a topologically exact sequence (*) exists iff α is stable, i.e. .
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