Fully absolutely summing and Hilbert-Schmidt multilinear mappings.

Mário C. Matos

Collectanea Mathematica (2003)

  • Volume: 54, Issue: 2, page 111-136
  • ISSN: 0010-0757

Abstract

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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.

How to cite

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Matos, Mário C.. "Fully absolutely summing and Hilbert-Schmidt multilinear mappings.." Collectanea Mathematica 54.2 (2003): 111-136. <http://eudml.org/doc/43048>.

@article{Matos2003,
abstract = {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.},
author = {Matos, Mário C.},
journal = {Collectanea Mathematica},
keywords = {Operador absolutamente sumante; Aplicación multilineal; Espacios de Banach; fully absolutely summing multilinear mappings; Banach spaces; virtually nuclear mappings},
language = {eng},
number = {2},
pages = {111-136},
title = {Fully absolutely summing and Hilbert-Schmidt multilinear mappings.},
url = {http://eudml.org/doc/43048},
volume = {54},
year = {2003},
}

TY - JOUR
AU - Matos, Mário C.
TI - Fully absolutely summing and Hilbert-Schmidt multilinear mappings.
JO - Collectanea Mathematica
PY - 2003
VL - 54
IS - 2
SP - 111
EP - 136
AB - 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.
LA - eng
KW - Operador absolutamente sumante; Aplicación multilineal; Espacios de Banach; fully absolutely summing multilinear mappings; Banach spaces; virtually nuclear mappings
UR - http://eudml.org/doc/43048
ER -

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