Characterizing Fréchet-Schwartz spaces via power bounded operators

Angela A. Albanese, José Bonet, and Werner J. Ricker. "Characterizing Fréchet-Schwartz spaces via power bounded operators." Studia Mathematica 224.1 (2014): 25-45. <http://eudml.org/doc/285520>.

@article{AngelaA2014,
abstract = {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.},
author = {Angela A. Albanese, José Bonet, Werner J. Ricker},
journal = {Studia Mathematica},
keywords = {power bounded operator; mean ergodic operator; Fréchet-Schwartz space; Köthe echelon space; Schauder decomposition; rapid convergence},
language = {eng},
number = {1},
pages = {25-45},
title = {Characterizing Fréchet-Schwartz spaces via power bounded operators},
url = {http://eudml.org/doc/285520},
volume = {224},
year = {2014},
}

TY - JOUR
AU - Angela A. Albanese
AU - José Bonet
AU - Werner J. Ricker
TI - Characterizing Fréchet-Schwartz spaces via power bounded operators
JO - Studia Mathematica
PY - 2014
VL - 224
IS - 1
SP - 25
EP - 45
AB - 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.
LA - eng
KW - power bounded operator; mean ergodic operator; Fréchet-Schwartz space; Köthe echelon space; Schauder decomposition; rapid convergence
UR - http://eudml.org/doc/285520
ER -