Geodesic
On the Maximal Operator Ideal Associated with a Tensor Norm Defined by Interpolation Spaces
Canadian mathematical bulletin, Tome 53 (2010) no. 4, pp. 690-705

Voir la notice de l'article provenant de la source Cambridge

DOI

The classical approach to studying operator ideals using tensor norms mainly focuses on those tensor norms and operator ideals defined by means of ${{l}_{p}}$ spaces. In a previous paper, an interpolation space, defined via the real method and using ${{l}_{p}}$ spaces, was used to define a tensor norm, and the associated minimal operator ideals were characterized. In this paper, the next natural step is taken, that is, the corresponding maximal operator ideals are characterized. As an application, necessary and sufficient conditions for the coincidence of the maximal and minimal ideals are given. Finally, the previous results are used in order to find some new metric properties of the mentioned tensor norm.
DOI : 10.4153/CMB-2010-075-6
Mots-clés : 46M05, 46M35, 46A32, maximal operator ideals, ultraproducts of spaces, interpolation spaces 
Puerta, M. E.; Loaiza, G. On the Maximal Operator Ideal Associated with a Tensor Norm Defined by Interpolation Spaces. Canadian mathematical bulletin, Tome 53 (2010) no. 4, pp. 690-705. doi: 10.4153/CMB-2010-075-6
@article{10_4153_CMB_2010_075_6,
     author = {Puerta, M. E. and Loaiza, G.},
     title = {On the {Maximal} {Operator} {Ideal} {Associated} with a {Tensor} {Norm} {Defined} by {Interpolation} {Spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {690--705},
     year = {2010},
     volume = {53},
     number = {4},
     doi = {10.4153/CMB-2010-075-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-075-6/}
}
TY  - JOUR
AU  - Puerta, M. E.
AU  - Loaiza, G.
TI  - On the Maximal Operator Ideal Associated with a Tensor Norm Defined by Interpolation Spaces
JO  - Canadian mathematical bulletin
PY  - 2010
SP  - 690
EP  - 705
VL  - 53
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-075-6/
DO  - 10.4153/CMB-2010-075-6
ID  - 10_4153_CMB_2010_075_6
ER  - 
%0 Journal Article
%A Puerta, M. E.
%A Loaiza, G.
%T On the Maximal Operator Ideal Associated with a Tensor Norm Defined by Interpolation Spaces
%J Canadian mathematical bulletin
%D 2010
%P 690-705
%V 53
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-075-6/
%R 10.4153/CMB-2010-075-6
%F 10_4153_CMB_2010_075_6

Cité par Sources :