Barrelledness of Lb(E,X) given a Banach space X and a Köthe sequence space E

Autores: M. Angeles Miñarro
Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 43, Fasc. 3, 1992, págs. 235-241
Idioma: inglés
Títulos paralelos:
- Tonelación de Lb(E,X) dados un espacio de Banach X y un espacio sucesional de Köthe E
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Resumen
- Given a Banach space $X$ and a Köthe sequence space $\lambda_p$, with $1\leq p ?\infty$ or $p\quad 0$, is is known that $L_b(\lambda_p,X)$ is barrelled if $\lambda_p$ satisfies Heinrich's density condition. In this note we show that if $p?1$ is barrelled if and only if every continuous linear operator from $\lambda_p$ into $X$ is compact. As a consequence we get a characterization of the distinguished spaces of type $\ell_\infty\hat{\otimes}_\pi\lambda_p$.