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.