$C_0$-semigroups and mean ergodic operators in a class of Fréchet spaces

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Abstract

It is shown that the generator of every exponentially equicontinuous, uniformly continuous $C_0$--semigroup of operators in the class of quojection Fréchet spaces $X$ (which includes properly all countable products of Banach spaces) is necessarily everywhere defined and continuous. If, in addition, $X$ is a Grothendieck space with the Dunford--Pettis property, then uniform continuity can be relaxed to strong continuity. Two results, one of M. Lin and one of H.P. Lotz, both concerned with uniformly mean ergodic operators in Banach spaces, are also extended to the class of Fréchet spaces mentioned above. They fail to hold for arbitrary Fréchet spaces.

Autore Pugliese

Tutti gli autori

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

Titolo volume/Rivista

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Anno di pubblicazione

2010

ISSN

0022-247X

ISBN

Non Disponibile

Numero di citazioni Wos

Nessuna citazione

Ultimo Aggiornamento Citazioni

Non Disponibile

Numero di citazioni Scopus

19

Ultimo Aggiornamento Citazioni

28/04/2018

Settori ERC

Non Disponibile

Codici ASJC

Non Disponibile