Abstract

We exhibit examples of Fréchet Montel spaces $E$ which have a non-reflexive Fréchet quotient but such that every Banach quotient is finite dimensional. The construction uses a method developed by Albanese and Moscatelli and requires new ingredients. Some of the main steps in the proof are presented in Section 2, they are of independent interest and show for example that the canonical inclusion between James spaces $J_p subset J_q, 1 < p < q < infty,$ is strictly cosingular. This result requires a careful analysis of the block basic sequences of the canonical basis of the dual $J'_p$ of the James space $J_p$, and permits us to show that the Fréchet space $J_{p^+} = cap_{q>p}J_q$ has no infinite-dimensional Banach quotients. Plichko and Maslyuchenko had proved that it has no infinite-dimensional Banach subspaces.

Autore Pugliese

• Albanese Angela Anna

Tutti gli autori

• A. A. Albanese , J. Bonet

Titolo volume/Rivista

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Anno di pubblicazione

2012

ISSN

0022-247X

ISBN

Non Disponibile

Numero di citazioni Wos

Nessuna citazione

Ultimo Aggiornamento Citazioni

Non Disponibile

Numero di citazioni Scopus

Non Disponibile

0

Ultimo Aggiornamento Citazioni

28/04/2018

Settori ERC

Non Disponibile

Codici ASJC

Non Disponibile