Fully absolutely summing and Hilbert-Schmidt multilinear mappings

• Autores: Mario C. Matos
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 54, Fasc. 2, 2003, págs. 111-136
• Idioma: inglés
• Títulos paralelos:
  • Aplicaciones completa y absolutamente sumantes y aplicaciones multilineales de Hilbert-Schmidt
• Enlaces
  • Texto completo
• Resumen

  • The space of the fully absolutely (r;r1,...,rn)-summing n-linear mappings between Banach spaces is introduced along with a natural (quasi-)norm on it. If r,rk C [1,+infinite], k=1,...,n, this space is characterized as the topological dual of a space of virtually nuclear mappings. Other examples and properties are considered and a relationship with a topological tensor product is stablished. For Hilbert spaces and r = r1 = ... = rn C [2,+infinite[ this space is isomorphic to the space of the Hilbert-Schmidt multilinear mappings.

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