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.
@article{urn:eudml:doc:43048,
title = {Fully absolutely summing and Hilbert-Schmidt multilinear mappings.},
journal = {Collectanea Mathematica},
volume = {54},
year = {2003},
pages = {111-136},
zbl = {1078.46031},
mrnumber = {MR1995136},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:43048}
}
Matos, Mário C. Fully absolutely summing and Hilbert-Schmidt multilinear mappings.. Collectanea Mathematica, Tome 54 (2003) pp. 111-136. http://gdmltest.u-ga.fr/item/urn:eudml:doc:43048/