Resumen de Barrelledness of Lb(E,X) given a Banach space X and a Köthe sequence space E
M. Angeles Miñarro
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 $\ell_\infty\hat{\otimes}_\pi\lambda_p$.
