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

top
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

top

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 -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.