Geodesic
Stability Results of Diameter Two Properties
Journal of convex analysis, Tome 22 (2015) no. 1, pp. 1-17
Cet article a éte moissonné depuis la source Heldermann Verlag

Voir la notice de l'article

A Banach space has the diameter two property if every (nonempty) weakly open set of its unit ball has diameter two. We prove that this property is stable under finite sums, whenever an absolute norm is considered in the product space, improving some previous results. Recently T. A. Abrahamsen, V. Lima and O. Nygaard [J. Convex Analysis 20 (2013) 329--338] defined the so-called strong diameter two property, i.e. every convex combination of slices in the unit ball has diameter two.
Classification : 46B20, 46B22
Mots-clés : Banach space, weakly open set, slice, absolute norm, diameter two property, Radon-Nikodym property 
@article{JCA_2015_22_1_JCA_2015_22_1_a0,
     author = {M. D. Acosta and J. Becerra-Guerrero and G. L\'opez-P\'erez},
     title = {Stability {Results} of {Diameter} {Two} {Properties}},
     journal = {Journal of convex analysis},
     pages = {1--17},
     year = {2015},
     volume = {22},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2015_22_1_JCA_2015_22_1_a0/}
}
TY  - JOUR
AU  - M. D. Acosta
AU  - J. Becerra-Guerrero
AU  - G. López-Pérez
TI  - Stability Results of Diameter Two Properties
JO  - Journal of convex analysis
PY  - 2015
SP  - 1
EP  - 17
VL  - 22
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/JCA_2015_22_1_JCA_2015_22_1_a0/
ID  - JCA_2015_22_1_JCA_2015_22_1_a0
ER  - 
%0 Journal Article
%A M. D. Acosta
%A J. Becerra-Guerrero
%A G. López-Pérez
%T Stability Results of Diameter Two Properties
%J Journal of convex analysis
%D 2015
%P 1-17
%V 22
%N 1
%U http://geodesic.mathdoc.fr/item/JCA_2015_22_1_JCA_2015_22_1_a0/
%F JCA_2015_22_1_JCA_2015_22_1_a0
M. D. Acosta; J. Becerra-Guerrero; G. López-Pérez. Stability Results of Diameter Two Properties. Journal of convex analysis, Tome 22 (2015) no. 1, pp. 1-17. http://geodesic.mathdoc.fr/item/JCA_2015_22_1_JCA_2015_22_1_a0/