A semigroup analogue of the Fonf-Lin-Wojtaszczyk ergodic characterization of reflexive Banach spaces with a basis

Delio Mugnolo. "A semigroup analogue of the Fonf-Lin-Wojtaszczyk ergodic characterization of reflexive Banach spaces with a basis." Studia Mathematica 164.3 (2004): 243-251. <http://eudml.org/doc/284780>.

@article{DelioMugnolo2004,
abstract = { In analogy to a recent result by V. Fonf, M. Lin, and P. Wojtaszczyk, we prove the following characterizations of a Banach space X with a basis. (i) X is finite-dimensional if and only if every bounded, uniformly continuous, mean ergodic semigroup on X is uniformly mean ergodic. (ii) X is reflexive if and only if every bounded strongly continuous semigroup is mean ergodic if and only if every bounded uniformly continuous semigroup on X is mean ergodic. },
author = {Delio Mugnolo},
journal = {Studia Mathematica},
keywords = {Schauder basis; reflexive Banach spaces; ergodic semigroups of operators},
language = {eng},
number = {3},
pages = {243-251},
title = {A semigroup analogue of the Fonf-Lin-Wojtaszczyk ergodic characterization of reflexive Banach spaces with a basis},
url = {http://eudml.org/doc/284780},
volume = {164},
year = {2004},
}

TY - JOUR
AU - Delio Mugnolo
TI - A semigroup analogue of the Fonf-Lin-Wojtaszczyk ergodic characterization of reflexive Banach spaces with a basis
JO - Studia Mathematica
PY - 2004
VL - 164
IS - 3
SP - 243
EP - 251
AB - In analogy to a recent result by V. Fonf, M. Lin, and P. Wojtaszczyk, we prove the following characterizations of a Banach space X with a basis. (i) X is finite-dimensional if and only if every bounded, uniformly continuous, mean ergodic semigroup on X is uniformly mean ergodic. (ii) X is reflexive if and only if every bounded strongly continuous semigroup is mean ergodic if and only if every bounded uniformly continuous semigroup on X is mean ergodic.
LA - eng
KW - Schauder basis; reflexive Banach spaces; ergodic semigroups of operators
UR - http://eudml.org/doc/284780
ER -