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Cesàro wedge and weak Cesàro wedge F K -spaces

H. G. Ince (2002)

Czechoslovak Mathematical Journal

In this paper we deal with Cesàro wedge and weak Cesàro wedge F K -spaces, and give several characterizations. Some applications of these spaces to general summability domains are also studied.

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...

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