Geometrical Aspects of Functional Analysis: Israel Seminar, 1985–86

M. Gromov (auth.), Joram Lindenstrauss, Vitali D. Milman (eds.)3540181032, 9783540181033, 0387181032

These are the proceedings of the Israel Seminar on the Geometric Aspects of Functional Analysis (GAFA) which was held between October 1985 and June 1986. The main emphasis of the seminar was on the study of the geometry of Banach spaces and in particular the study of convex sets in and infinite-dimensional spaces. The greater part of the volume is made up of original research papers; a few of the papers are expository in nature. Together, they reflect the wide scope of the problems studied at present in the framework of the geometry of Banach spaces.

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Table of contents :
Monotonicity of the volume of intersection of balls….Pages 1-4
On lattice packing of convex symmetric sets in ℜ n ….Pages 5-12
Diameter of a minimal invariant subset of equivariant lipschitz actions on compact subsets of ℝ k ….Pages 13-20
The relation between the distance and the weak distance for spaces with a symmetric basis….Pages 21-38
Complements of subspaces of ℓ p n ; p ≥1 which are uniquely determined….Pages 39-52
Embedding X p m spaces into ℓ r n ….Pages 53-74
Some remarks on Urysohn’s inequality and volume ratio of cotype 2-spaces….Pages 75-81
On the covering numbers of convex bodies….Pages 82-95
On a theorem of J. Bourgain on finite dimensional decompositions and the radon-nikodym property….Pages 96-112
Sudakov type inequalities for convex bodies in IR n ….Pages 113-121
An application of infinite dimensional holomorphy to the geometry of banach spaces….Pages 122-150
A density condition for analyticity of the restriction algebra….Pages 151-156
Remarks on the extension of lipschitz maps defined on discrete sets and uniform homeomorphisms….Pages 157-167
On dimension free maximal inequalities for convex symmetric bodies in ℜ n ….Pages 168-176
On lipschitz embedding of finite metric spaces in low dimensional normed spaces….Pages 177-184
Random series in the real interpolation spaces between the spaces v p ….Pages 185-209
Cotype of the spaces ( A 0 , A 1 ) θ1 ….Pages 210-212