Geodesic
Auerbach Bases and Minimal Volume Sufficient Enlargements
Canadian mathematical bulletin, Tome 54 (2011) no. 4, pp. 726-738

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

DOI

Let ${{B}_{Y}}$ denote the unit ball of a normed linear space $Y$ . A symmetric, bounded, closed, convex set $A$ in a finite dimensional normed linear space $X$ is called a sufficient enlargement for $X$ if, for an arbitrary isometric embedding of $X$ into a Banach space $Y$ , there exists a linear projection $P:\,Y\,\to \,X$ such that $P({{B}_{Y}})\,\subset \,A$ . Each finite dimensional normed space has a minimal-volume sufficient enlargement that is a parallelepiped; some spaces have “exotic” minimal-volume sufficient enlargements. The main result of the paper is a characterization of spaces having “exotic” minimal-volume sufficient enlargements in terms of Auerbach bases.
DOI : 10.4153/CMB-2011-043-3
Mots-clés : 46B07, 52A21, 46B15 
Ostrovskii, M. I. Auerbach Bases and Minimal Volume Sufficient Enlargements. Canadian mathematical bulletin, Tome 54 (2011) no. 4, pp. 726-738. doi: 10.4153/CMB-2011-043-3
@article{10_4153_CMB_2011_043_3,
     author = {Ostrovskii, M. I.},
     title = {Auerbach {Bases} and {Minimal} {Volume} {Sufficient} {Enlargements}},
     journal = {Canadian mathematical bulletin},
     pages = {726--738},
     year = {2011},
     volume = {54},
     number = {4},
     doi = {10.4153/CMB-2011-043-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-043-3/}
}
TY  - JOUR
AU  - Ostrovskii, M. I.
TI  - Auerbach Bases and Minimal Volume Sufficient Enlargements
JO  - Canadian mathematical bulletin
PY  - 2011
SP  - 726
EP  - 738
VL  - 54
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-043-3/
DO  - 10.4153/CMB-2011-043-3
ID  - 10_4153_CMB_2011_043_3
ER  - 
%0 Journal Article
%A Ostrovskii, M. I.
%T Auerbach Bases and Minimal Volume Sufficient Enlargements
%J Canadian mathematical bulletin
%D 2011
%P 726-738
%V 54
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-043-3/
%R 10.4153/CMB-2011-043-3
%F 10_4153_CMB_2011_043_3

Cité par Sources :