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
• Enlaces
  • Texto completo
• 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.

• Referencias bibliográficas
  • J.S. Cohen, Absolutely $p$-summing, $p$-nuclear operators and their conjugates, Math. Ann. 201 (1973), 177–200.
  • G.J.O. Jameson, Summing and Nuclear Norms in Banach Space Theory, London Math. Soc. Students Texts 8, Cambridge University Press, 1987.
  • J. Lindenstrauss and A. Pełczynski, Absolutely summing operators in $L\_p$-spaces and their applications, Studia Math. 29 (1968), 275–326.
  • J.S. Morell and J.R. Retherford, $p$-trivial Banach spaces, Studia Math. 43 (1972), 1–25.
  • A. Pietsch, Absolut $p$-summierende Abbildungen in normierten Räumen, Studia Math. 28 (1967), 333–353.
  • A. Pietsch, Operator Ideals, North-Holland, 1980.
  • C.P. Stegall and J.R. Retherford, Fully nuclear and completely nuclear operators with applications to $L\_1$ and $L\_\infty$ spaces, Transactions...
  • N. Tomczak-Jaegermann, Banach-Mazur Distances and Finite-Dimensional Operator Ideals, Pitman Monographs and Surveys in Pure and Appl. Math....