A note on absolutely p-summing operators

• Autores: Cándido Piñeiro Gómez
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 45, Fasc. 2, 1994, págs. 133-136
• Idioma: inglés
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• Resumen

  • Let $X, Y$ be Banach spaces. If $X$ is a $\mathcal{D}_q$-space ($1 < q\leq +\infty$) we prove that $\Pi^d_p (X, Y )\subset\Pi_p(X, Y )$ if and only if $Y$ is isomorphic to a subspace of an $L^p$-space, where $p$ is the conjugate number for $q$. We also prove that, if $Y$ is a $\mathcal{D}_p$-space, $\Pi_p(X, Y )\subset\Pi^d_p (X, Y )$ if and only if $X^\ast$ is isomorphic to a subspace of an $L^p$-space.