Grothendieck spaces with the Dunford-Pettis property

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Abstract

Banach spaces which are Grothendieck spaces with the Dunford-Pettis property (briefly, GDP) are classical. A systematic treatment of GDP-Fréchet spaces occurs in Bonet and Ricker (Positivity 11.77-93, 2007). This investigation is continued here for locally convex Hausdorff spaces. The product and (most) inductive limits of GDP-spaces are again GDP-spaces. Also, every complete injective space is a GDP-space. For $pin {0}cup [1,infty)$ it is shown that the classical co-echelon spaces $k_p(V)$ and $K_p(ov{V})$ are GDP-spaces if and only if they are Montel. On the other hand, $K_infty(ov{V})$ is always a GDP-space and $k_infty(V)$ is a GDP-space whenever its (Fréchet) predual, i.e., the Kothe echelon space $lambda_1(A)$, is distinguished.

Autore Pugliese

Tutti gli autori

  • A. ALBANESE , BONET J. , RICKER W.J.

Titolo volume/Rivista

POSITIVITY

Anno di pubblicazione

2010

ISSN

1385-1292

ISBN

Non Disponibile

Numero di citazioni Wos

Nessuna citazione

Ultimo Aggiornamento Citazioni

Non Disponibile

Numero di citazioni Scopus

9

Ultimo Aggiornamento Citazioni

28/04/2018

Settori ERC

Non Disponibile

Codici ASJC

Non Disponibile