Geodesic
Norm attaining bilinear forms on $C^{\ast }$-algebras
J. Alaminos1 ; R. Payá2 ; A. R. Villena2
1 Departamento de Análisis Matemático Facultad de Ciencias Universidad de Granada 18071 Granada, Spain
2 Departamento de Análisis Matemático. Facultad de Ciencias Universidad de Granada 18071 Granada, Spain
Studia Mathematica, Tome 157 (2003) no. 1, pp. 47-56

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We give a sufficient condition on a $C^{*}$-algebra to ensure that every weakly compact operator into an arbitrary Banach space can be approximated by norm attaining operators and that every continuous bilinear form can be approximated by norm attaining bilinear forms. Moreover we prove that the class of $C^{\ast }$-algebras satisfying this condition includes the group $C^{\ast }$-algebras of compact groups.
DOI : 10.4064/sm157-1-4
Keywords: sufficient condition * algebra ensure every weakly compact operator arbitrary banach space approximated norm attaining operators every continuous bilinear form approximated norm attaining bilinear forms moreover prove class ast algebras satisfying condition includes group ast algebras compact groups

J. Alaminos 1 ; R. Payá 2 ; A. R. Villena 2

1 Departamento de Análisis Matemático Facultad de Ciencias Universidad de Granada 18071 Granada, Spain
2 Departamento de Análisis Matemático. Facultad de Ciencias Universidad de Granada 18071 Granada, Spain 
@article{10_4064_sm157_1_4,
     author = {J. Alaminos and R. Pay\'a and A. R. Villena},
     title = {Norm attaining bilinear forms on $C^{\ast }$-algebras},
     journal = {Studia Mathematica},
     pages = {47--56},
     publisher = {mathdoc},
     volume = {157},
     number = {1},
     year = {2003},
     doi = {10.4064/sm157-1-4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm157-1-4/}
}
TY  - JOUR
AU  - J. Alaminos
AU  - R. Payá
AU  - A. R. Villena
TI  - Norm attaining bilinear forms on $C^{\ast }$-algebras
JO  - Studia Mathematica
PY  - 2003
SP  - 47
EP  - 56
VL  - 157
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm157-1-4/
DO  - 10.4064/sm157-1-4
LA  - en
ID  - 10_4064_sm157_1_4
ER  - 
%0 Journal Article
%A J. Alaminos
%A R. Payá
%A A. R. Villena
%T Norm attaining bilinear forms on $C^{\ast }$-algebras
%J Studia Mathematica
%D 2003
%P 47-56
%V 157
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/sm157-1-4/
%R 10.4064/sm157-1-4
%G en
%F 10_4064_sm157_1_4
J. Alaminos; R. Payá; A. R. Villena. Norm attaining bilinear forms on $C^{\ast }$-algebras. Studia Mathematica, Tome 157 (2003) no. 1, pp. 47-56. doi: 10.4064/sm157-1-4

Cité par Sources :