## Functiones et Approximatio Commentarii Mathematici

### A Banach function space $X$ for which all operators from $\ell^p$ to $X$ are compact

#### Abstract

We construct a rearrangement invariant space $X$ on $[0,1]$ with the property that all bounded linear operators from $\ell^p$, $1<p<\infty$, to $X$ are compact, but there exists a non-compact operator from $\ell^\infty$ to $X$. The techniques used allow to give a new proof of the characterization given by Hern\'andez, Raynaud and Semenov of the rearrangement invariant spaces on $[0,1]$ for which the canonical embedding into $L^1([0,1])$ is finitely strictly singular.

#### Article information

Source
Funct. Approx. Comment. Math., Volume 50, Number 2 (2014), 233-249.

Dates
First available in Project Euclid: 26 June 2014

https://projecteuclid.org/euclid.facm/1403811842

Digital Object Identifier
doi:10.7169/facm/2014.50.2.3

Mathematical Reviews number (MathSciNet)
MR3229059

Zentralblatt MATH identifier
1304.28014

#### Citation

Curbera, Guillermo P.; Rodríguez-Piazza, Luis. A Banach function space $X$ for which all operators from $\ell^p$ to $X$ are compact. Funct. Approx. Comment. Math. 50 (2014), no. 2, 233--249. doi:10.7169/facm/2014.50.2.3. https://projecteuclid.org/euclid.facm/1403811842

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