Quotients of Essentially Euclidean Spaces
Canadian mathematical bulletin, Tome 62 (2019) no. 1, pp. 71-74

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

A precise quantitative version of the following qualitative statement is proved: If a finite-dimensional normed space contains approximately Euclidean subspaces of all proportional dimensions, then every proportional dimensional quotient space has the same property.
DOI : 10.4153/CMB-2017-038-x
Mots-clés : essentially euclidean
Figiel, Tadeusz; Johnson, William. Quotients of Essentially Euclidean Spaces. Canadian mathematical bulletin, Tome 62 (2019) no. 1, pp. 71-74. doi: 10.4153/CMB-2017-038-x
@article{10_4153_CMB_2017_038_x,
     author = {Figiel, Tadeusz and Johnson, William},
     title = {Quotients of {Essentially} {Euclidean} {Spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {71--74},
     year = {2019},
     volume = {62},
     number = {1},
     doi = {10.4153/CMB-2017-038-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-038-x/}
}
TY  - JOUR
AU  - Figiel, Tadeusz
AU  - Johnson, William
TI  - Quotients of Essentially Euclidean Spaces
JO  - Canadian mathematical bulletin
PY  - 2019
SP  - 71
EP  - 74
VL  - 62
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-038-x/
DO  - 10.4153/CMB-2017-038-x
ID  - 10_4153_CMB_2017_038_x
ER  - 
%0 Journal Article
%A Figiel, Tadeusz
%A Johnson, William
%T Quotients of Essentially Euclidean Spaces
%J Canadian mathematical bulletin
%D 2019
%P 71-74
%V 62
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-038-x/
%R 10.4153/CMB-2017-038-x
%F 10_4153_CMB_2017_038_x

[BKT] Bourgain, J., Kalton, N. J., and Tzafriri, L., Geometry of finite-dimensional subspaces and quotients of L . In: Geometric aspects of functional analysis (1987–88), Lecture Notes in Math., 1376, Springer, Berlin, 1989, pp. 138–175. . Google Scholar | DOI

[Day] Day, M. M., On the basis problem in normed spaces . Proc. Amer. Math. Soc. 13(1962), 655–658. . Google Scholar | DOI

[JS] Johnson, W. B. and Schechtman, G., Very tight embeddings of subspaces of L , 1⩽p < 2, into n . Geom. Funct. Anal. 13(2003), no. 4, 845–851. . Google Scholar | DOI

[KKM] Krein, M. G., Milman, D. P., and Krasnosel’Ski, M. A., On the defect numbers of linear operators in Banach space and some geometric questions . (Russian) Sbornik Trudov Inst. Acad. NAUK Uk. SSR 11(1948), 97–112. Google Scholar

[LMT-J] Litvak, A. E., Milman, V. D., and Tomczak-Jaegermann, N., Essentially-Euclidean convex bodies . Studia Math. 196(2010), no. 3, 207–221. . Google Scholar | DOI

[Mil] Milman, V. D., Almost Euclidean quotient spaces of subspaces of a finite-dimensional normed space . Proc. Amer. Math. Soc. 94(1985), no. 3, 445–449. . Google Scholar | DOI

[Pis] Pisier, G., The volume of convex bodies and Banach space geometry. Cambridge Tracts in Mathematics, 94, Cambridge University Press, Cambridge, 1989. . Google Scholar | DOI

Cité par Sources :