Revistes Catalanes amb Accés Obert (RACO)

Barrelledness of $L_b(\lambda_p,X)$

M. Ángeles 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 $\ell_\infty\hat{\otimes}_\pi\lambda_p$.

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