Geometric Aspects of Functional Analysis

1. Front Matter

   Pages N2-VIII

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2. The transportation cost for the cube

   • M. Anttila

   Pages 1-11

3. The uniform concentration of measure phenomenon in ℓ ⁿ _p (1 ≤ p ≤ 2)

   • J. Arias-de-Reyna, R. Villa

   Pages 13-18

4. An editorial comment on the preceding paper

   • G. Schechtman

   Pages 19-20

5. A remark on the slicing problem

   • K. Ball

   Pages 21-26

6. Remarks on the growth of L ^p-norms of polynomials

   • S. G. Bobkov

   Pages 27-35

7. Positive lyapounov exponents for most energies

   • J. Bourgain

   Pages 37-66

8. Anderson localization for the band model

   • J. Bourgain, S. Jitomirskaya

   Pages 67-79

9. Convex bodies with minimal mean width

   • A. A. Giannopoulos, V. D. Milman, M. Rudelson

   Pages 81-93

10. Euclidean projections of a p-convex body

    • O. Guédon, A. E. Litvak

    Pages 95-108

11. Remarks on minkowski symmetrizations

    • B. Klartag

    Pages 109-117

12. Average volume of sections of star bodies

    • A. Koldobsky, M. Lifshits

    Pages 119-146

13. Between sobolev and poincaré

    • R. Latała, K. Oleszkiewicz

    Pages 147-168

14. Random aspects of high-dimensional convex bodies

    • A. E. Litvak, N. Tomczak-Jaegermann

    Pages 169-190

15. A geometric lemma and duality of entropy numbers

    • V. D. Milman, S. J. Szarek

    Pages 191-222

16. Stabilized asymptotic structures and envelopes in banach spaces

    • V. D. Milman, N. Tomczak-Jaegermann

    Pages 223-237

17. On the isotropic constant of Non-symmetric convex bodies

    • G. Paouris

    Pages 239-243

18. Concentration on the ℓ ⁿ _p ball

    • G. Schechtman, J. Zinn

    Pages 245-256

19. Shannon’s entropy power inequality via restricted minkowski sums

    • S. J. Szarek, D. Voiculescu

    Pages 257-262

20. Notes on an inequality by pisier for functions on the discrete cube

    • R. Wagner

    Pages 263-268

This volume of original research papers from the Israeli GAFA seminar during the years 1996-2000 not only reports on more traditional directions of Geometric Functional Analysis, but also reflects on some of the recent new trends in Banach Space Theory and related topics. These include the tighter connection with convexity and the resulting added emphasis on convex bodies that are not necessarily centrally symmetric, and the treatment of bodies which have only very weak convex-like structure. Another topic represented here is the use of new probabilistic tools; in particular transportation of measure methods and new inequalities emerging from Poincaré-like inequalities.

• Banach space
• Dimension
• Power
• Trend
• asymptotic geometric analysis
• convexity
• functional analysis
• local theory of Banach spaces

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