Abstract

The Banach spaces $ces(p)$, $1<p<infty$, were intensively studied by G. Bennett and others. The largest solid Banach lattice in $mathbb{C}^{mathbb {N}}$ which contains $ell_p$ and which the Cesàro operator $C colonmathbb{C}^{mathbb {N}}tomathbb{C}^{mathbb {N}}$ maps into $ell_p$ is $ces(p)$. For each $1leq p<infty$, the (positive) operator $C$ also maps the Fréchet space $ell_{p+}=cap_{q>p}ell_q} into itself. It is shown that the largest solid Fréchet lattice in $mathbb{C}^{mathbb {N}$ which contains $ell_{p+} and which $C$ maps into $ell_{p+} is precisely $ces(p+) :=cap_{q>p}ces(q)$. Although the spaces $ell_{p+}$ are well understood, it seems that the spaces $ces(p+)$ have not been considered at all. A detailed study of the Fréchet spaces $ces(p+)$, $1leq p<infty$, is undertaken. They are very different to the Fréchet spaces $ell_{p+}$ which generate them in the above sense. We prove that each $ces(p+)$ is a power series space of finite type and order one, and that all the spaces $ces(p+)$, $1leq p<infty$, are isomorphic.

Autore Pugliese

• Albanese Angela Anna

Tutti gli autori

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

Titolo volume/Rivista

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Anno di pubblicazione

2018

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

26/04/2018

Settori ERC

Non Disponibile

Codici ASJC

Non Disponibile