Random spaces generated by vertices of the cube

Discrete and Computational Geometry

Volumn 28, Issue 2, 2002, Pages 255-273

  Giannopoulos, Apostolos ^a   Hartzoulaki, Marianna ^a  

^a UNIVERSITY OF CRETE   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036025567     PISSN: 01795376     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00454-002-2779-3     Document Type: Article

References (37)

1. K. M. Ball, Normed Spaces with a Weak Gordon-Lewis Property, Lecture Notes in Mathematics 1470, Springer-Verlag, Berlin (1991), pp. 36-47.
2. K. Ball and A. Pajor, Convex bodies with few faces, Proc. Amer. Math. Soc. 110 (1990), 225-231.
3. I. Barany and Z. Furedi, Computing the volume is difficult, Discrete Comput. Geom. 2 (1987), 319-326.
4. I. Barany and A. Por, On 0-1 polytopes with many facets, Adv. in Math. 161 (2001), 209-228.
5. Y. Benyamini and Y. Gordon, Random factorization of operators between Banach spaces, J. Analyse Math. 39 (1981), 45-74.
6. J. Bourgain, On the Distribution of Polynomials on High Dimensional Convex Sets, Lecture Notes in Mathematics 1469, Springer-Verlag, Berlin (1991), pp. 127-137.
7. J. Bourgain and V. D. Milman, Distances between normed spaces, their subspaces and quotient spaces, Integral Equations Operator Theory 9 (1986), 31-46.
8. J. Bourgain, J. Lindenstrauss and V. D. Milman, Approximation of zonoids by zonotopes, Acta Math. 162 (1989), 73-141.
9. B. Carl and A. Pajor, Gelfand numbers of operators with values in Hubert spaces, Invent. Math. 94 (1988), 459-504.
10. ̌ F. Application aux produits d'espaces de Wiener abstraits, Seminaire Maurey-Schwartz, Exp. 19, Ecole Polytechnique, Palaiseau (1977).
11. W. J. Davis, V. D. Milman and N. Tomczak-Jaegermann, The distance between certain n-dimensional spaces, Israel J. Math. 39 (1981), 1-15.
12. M. E. Dyer, Z. Furedi and C. McDiarmid, Volumes spanned by random points in the hypercube, Random Structures Algorithms 3 (1992), 91-106.
13. n, and estimates of the Gordon-Lewis constants, Israel J. Math. 37 (1980), 92-112.
14. T. Figiel and N. Tomczak-Jaegermann, Projections onto Hilbertian subspaces of Banach spaces, Israel J. Math. 33 (1979), 155-171.
15. T. Figiel, S. Kwapien and A. Pelczynski, Sharp estimates for the constants of local unconditional structure of Minkowski spaces, Bull. Acad. Polon. Sci. 25 (1977), 1221-1226.
16. T. Figiel, J. Lindenstrauss and V. D. Milman, The dimension of almost spherical sections of convex bodies, Acta Math. 139 (1977), 53-94.
17. A. A. Giannopoulos and V. D. Milman, Concentration property on probability spaces, Adv. in Math. 156 (2000), 77-106.
18. E. D. Gluskin, The diameter of the Minkowski compactum is approximately equal to n, Functional Anal. Appl. 15 (1981), 72-73.
19. E. D. Gluskin, Finite dimensional analogues of spaces without basis, Dokl. Akad. Nauk USSR 216 (1981), 1046-1050.
20. E. D. Gluskin, Extremal properties of orthogonal parallelepipeds and their applications to the geometry of Banach spaces, Math. USSR-Sbo. 64 (1989), 85-96.
21. F. John, Extremum Problems with Inequalities as Subsidiary Conditions, Courant Anniversary Volume, Interscience, New York (1948), pp. 187-204.
22. M. Junge, Proportional subspaces of spaces with unconditional basis have good volume properties, in Geometric Aspects of Functional Analysis, Operator Theory: Advances and Applications (eds. J. Lindenstrauss and V. D. Milman), Vol. 77, Birkhauser, Basel (1995), pp. 121-129.
23. B. S. Kashin, Sections of some finite-dimensional sets and classes of smooth functions, Izv. Akad. Nauk. SSSR Ser. Mat. 41 (1977), 334-351.
24. D. R. Lewis, Ellipsoids defined by Banach ideal norms, Mathematika 26 (1979), 18-29.
25. V. D. Milman and A. Pajor, Isotropic Position and Inertia Ellipsoids and Zonoids of the Unit Ball of a Normed n-Dimensional Space, Lecture Notes in Mathematics 1376, Springer-Verlag, Berlin (1989), pp. 64-104.
26. V. D. Milman and G. Schechtman, Asymptotic Theory of Finite Dimensional Named Spaces, Lecture Notes in Mathematics 1200, Springer-Verlag, Berlin (1986).
27. S. J. Montgomery-Smith, The distribution of Rademacher sums, Proc. Amer. Math. Soc. 109 (1990), 517-522.
28. A. Pietsch, Absolute p-summierende Abbildugen in normierten Raumen, Studia Math. 28 (1967), 333-353.
29. G. Pisier, Holomorphic semi-groups and the geometry of Banach spaces, Ann. of Math. 115 (1982), 375-392.
30. G. Pisier, The Volume of Convex Bodies and Banach Space Geometry, Cambridge Tracts in Mathematics 94, Cambridge University Press, Cambridge (1989).
31. G. Schechtman, Random embeddings of Euclidean spaces in sequence spaces, Israel J. Math. 40 (1981), 187-192.
32. n, Bull. Acad. Polon. Sci. 26 (1978), 691-694.
33. S. J. Szarek, The finite dimensional basis problem, with an appendix on nets of Grassman manifold, Acta Math. 159 (1983), 153-179.
34. n and random matrices, Amer. J. Math. 112 (1990), 899-942.
35. S. J. Szarek and N. Tomczak-Jaegermann, On nearly Euclidean decompositions of some classes of Banach spaces, Compositio Math. 40 (1980), 367-385.
36. n, Proc. Amer. Math. Soc. 72 (1978), 305-308.
37. N. Tomczak-Jaegermann, Banach-Mazur Distances and Finite Dimensional Operator Ideals, Pitman Monographs 38, Pitman, London (1989).