Skip to main content Accesibility Help

Quotients of Essentially Euclidean Spaces

  • Tadeusz Figiel (a1) and William Johnson (a2)

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.

Hide All

Author W. J. was supported in part by NSF DMS-1565826.

Hide All
[BKT] Bourgain, J., Kalton, N. J., and Tzafriri, L., Geometry of finite-dimensional subspaces and quotients of L p . In: Geometric aspects of functional analysis (1987–88), Lecture Notes in Math., 1376, Springer, Berlin, 1989, pp. 138175.
[Day] Day, M. M., On the basis problem in normed spaces . Proc. Amer. Math. Soc. 13(1962), 655658.
[JS] Johnson, W. B. and Schechtman, G., Very tight embeddings of subspaces of L p , 1⩽p < 2, into p n . Geom. Funct. Anal. 13(2003), no. 4, 845851.
[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), 97112.
[LMT-J] Litvak, A. E., Milman, V. D., and Tomczak-Jaegermann, N., Essentially-Euclidean convex bodies . Studia Math. 196(2010), no. 3, 207221.
[Mil] Milman, V. D., Almost Euclidean quotient spaces of subspaces of a finite-dimensional normed space . Proc. Amer. Math. Soc. 94(1985), no. 3, 445449.
[Pis] Pisier, G., The volume of convex bodies and Banach space geometry. Cambridge Tracts in Mathematics, 94, Cambridge University Press, Cambridge, 1989.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


MSC classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed