Abstract.
We prove several results of the following type: given finite dimensional normed space V there exists another space X with log dim X = O(log dim V) and such that every subspace (or quotient) of X, whose dimension is not “too small,” contains a further subspace isometric to V. This sheds new light on the structure of such large subspaces or quotients (resp. large sections or projections of convex bodies) and allows us to solve several problems stated in the 1980s by V. Milman.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Szarek, S.J., Tomczak-Jaegermann, N. Saturating constructions for normed spaces. GAFA, Geom. funct. anal. 14, 1352–1375 (2004). https://doi.org/10.1007/s00039-004-0495-2
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s00039-004-0495-2