The approximation property of order (p,q) in Banach spaces

• Autores: Juan Carlos Díaz Alcaide , Juan Antonio López Molina , María José Rivera Ortún
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 41, Fasc. 3, 1990, págs. 217-232
• Idioma: inglés
• Títulos paralelos:
  • La propiedad de aproximación de orden (p,q) en espacios de Banach
• Enlaces
  • Texto completo
• Resumen

  • We introduce the approximation property of order ($p,q$) in Banach spaces (in short $AP_{pq}$) to study topological properties of the space $D_{q'p'}(E,F)$ of ($q',p'$)-dominated operators between the Banach spaces $E$ and $F$. After some equivalent formulations of the $AP_{pq}$, we characterize the reflexivity of $D_{q'p'}(E,F)$ when $E$ has the $AP_{qp}$ or $F'$ has the $AP_{pq}$ and we give sufficient conditions for $E\hat\otimes_{\alpha_{pq}}F$ and $E\hat\otimes_{\alpha'_{pq}}F$ to be weakly sequentially complete.

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