论文信息 - Embedding subspaces of L1 into l1N

Embedding subspaces of L1 into l1N

We simplify techniques of Schechtman,Bourgain,Lindenstrauss,Milman, to prove the following: If X is an n-dimensional subspace of L 1 , there exists a subspace Y of l 1 N such that d(X,Y)≤1+e whenever N≥CK(X) 2 e −2 n, where K(X) is the K-convexity constant of X, and where C is a universal constant

M. Talagrand

[1] J. Hoffmann-jorgensen. Sums of independent Banach space valued random variables , 1974 .

[2] T. Figiel,et al. The dimension of almost spherical sections of convex bodies , 1976 .

[3] D. R. Lewis. Finite dimensional subspaces of $L_{p}$ , 1978 .

[4] G. Pisier,et al. Un théorème sur les opérateurs linéaires entre espaces de Banach qui se factorisent par un espace de Hilbert , 1980 .

[5] G. Pisier,et al. Random Fourier Series with Applications to Harmonic Analysis. , 1981 .

[6] William B. Johnson,et al. Embeddinglpm intol1n , 1982 .

[7] Y. Gordon. Some inequalities for Gaussian processes and applications , 1985 .

[8] J. Lindenstrauss,et al. Approximation of zonoids by zonotopes , 1989 .

[9] M. Ledoux,et al. Comparison Theorems, Random Geometry and Some Limit Theorems for Empirical Processes , 1989 .