Abstract

Let $(T(t))_{tgeq 0}$ be a strongly continuous $C_0$-semigroup of bounded linear operators on a Banach space $X$ such that $lim_{ttoinfty}||T(t)||/t = 0$. Characterizations of when $(T(t))_{tgeq 0}$ is uniformly mean ergodic, i.e., of when its Cesàro means $r^{-1}int_0^r T(s)ds$ converge in operator norm as $to infty$, are known. For instance, this is so if and only if the infinitesimal generator $A$ has closed range in $X$ if and only if $lim_{lambdato 0^+}lambda R(lambda, A)$ exists in the operator norm topology (where $R(lambda,A)$ is the resolvent operator of $A$ at $lambda$). These characterizations, and others, are shown to remain valid in the class of quojection Fréchet spaces, which includes all Banach spaces, countable products of Banach spaces, and many more. It is shown that the extension fails to hold for all Fréchet spaces. Applications of the results to concrete examples of $C_0$-semigroups in particular Fréchet function and sequence spaces are presented.

Autore Pugliese

• Albanese Angela Anna

Tutti gli autori

• A.A. Albanese , J. Bonet , W.J. Ricker

Titolo volume/Rivista

FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI

Anno di pubblicazione

2014

ISSN

0208-6573

ISBN

Non Disponibile

Numero di citazioni Wos

Nessuna citazione

Ultimo Aggiornamento Citazioni

Non Disponibile

Numero di citazioni Scopus

2

Ultimo Aggiornamento Citazioni

28/04/2018

Settori ERC

Non Disponibile

Codici ASJC

Non Disponibile