Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Almost Euclidean quotient spaces of subspaces of a finite-dimensional normed space

Author: V. D. Milman
Journal: Proc. Amer. Math. Soc. 94 (1985), 445-449
MSC: Primary 46B20
MathSciNet review: 787891
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The main result of this article is Theorem 1 which states that a quotient space $ Y,\dim Y = k$, of a subspace of any finite dimensional normed space $ X$, may be chosen to be $ d$-isomorphic to a euclidean space even for $ k = [\lambda n]$ for any fixed $ \lambda < 1$ (and $ d$ depending on $ \lambda $ only).

References [Enhancements On Off] (What's this?)

  • [F. T.] T. Figiel and N. Tomczak-Jaegermann, Projections onto Hilbertian subspaces of Banach spaces, Israel J. Math 33 (1979), 155-171. MR 571251 (81f:46024)
  • [K] B. S. Kashin, Diameters of some finite dimensional sets and of some classes of smooth functions, Izv. Akad. Nauk SSSR Ser. Math. 41 (1977), 334-351. (Russian) MR 0481792 (58:1891)
  • [M$ _{1}$] V. D. Milman, New proof of the theorem of Dvoretzky on sections of convex bodies, Functional Anal. Appl. 5 (1971), 28-37. (Russian) MR 0293374 (45:2451)
  • [M$ _{2}$] -, Geometrical inequalities and mixed volumes in local theory of Banach spaces, Colloque Laurent Schwartz, Soc. Math. France, 1985.
  • [P] G. Pisier, Remarques sur un resultat non publie de B. Maurey, Séminaire d'Analyse Fonctionnelle, 1980-1981, Exp. V. MR 659306 (83h:46026)
  • 1. -, $ K$-convexity, Proc. Res. Workshop on Banach Space Theory (Univ. of Iowa, 1981), pp. 139-151. MR 724111 (84k:46015)
  • [S] L. A. Santalo, Un invariante afin para los cuerpos convexos de espacios de $ n$ dimensiones, Portugal. Math. 8 (1949).
  • [Sz] S. J. Szarek, Volume estimates and nearly Euclidean decompositions for normed spaces, Séminaire d'Analyse Fonctionelle, 1979-1980, Exp. XXV. MR 604406 (82g:46041)
  • [U] P. S. Urysohn, Mean width and volume of convex bodies in an $ n$-dimensional space, Mat. Sb. 31 (1924), 477-486.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46B20

Retrieve articles in all journals with MSC: 46B20

Additional Information

Keywords: Finite-dimensional spaces, euclidean spaces
Article copyright: © Copyright 1985 American Mathematical Society

American Mathematical Society