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Characterizing Fréchet-Schwartz spaces via power bounded operators

Angela A. Albanese, José Bonet, Werner J. Ricker (2014)

Studia Mathematica

We characterize Köthe echelon spaces (and, more generally, those Fréchet spaces with an unconditional basis) which are Schwartz, in terms of the convergence of the Cesàro means of power bounded operators defined on them. This complements similar known characterizations of reflexive and of Fréchet-Montel spaces with a basis. Every strongly convergent sequence of continuous linear operators on a Fréchet-Schwartz space does so in a special way. We single out this type of "rapid convergence" for a sequence...

Continuous linear extension operators on spaces of holomorphic functions on closed subgroups of a complex Lie group

Do Duc Thai, Dinh Huy Hoang (1999)

Annales Polonici Mathematici

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 π 1 : V Γ is finite and proper, then R V : O ( Γ × G ) I m R V O ( V ) has a right inverse

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