Characterizing Fréchet-Schwartz spaces via power bounded operators

• Autorzy: Angela A. Albanese , José Bonet , Werner J. Ricker
• Języki publikacji: EN

Abstrakty

EN

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 of operators and study its relationship to the structure of the underlying space. Its relevance for Schauder decompositions and the connection to mean ergodic operators on Fréchet-Schwartz spaces is also investigated.

Kategorie tematyczne

• 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
• 47A35: Ergodic theory
• 46A04: Locally convex Fr\'echet spaces and (DF)-spaces
• 46A45: Sequence spaces (including K\"othe sequence spaces)
• 46A11: Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 224
• Numer: 1
• Strony: 25-45

Daty

wydano

2014

Twórcy

autor

Angela A. Albanese

• Dipartimento di Matematica e Fisica "E. De Giorgi", Università del Salento, C.P. 193, I-73100 Lecce, Italy

autor

José Bonet

• Instituto Universitario de Matemática Pura y Aplicada IUMPA, Universidad Politécnica de Valencia, E-46071 Valencia, Spain

autor

Werner J. Ricker

• Math.-Geogr. Fakultät, Katholische Universität Eichstätt-Ingolstadt, D-85072 Eichstätt, Germany

Identyfikatory

DOI

10.4064/sm224-1-2