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Book Review

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Book Information:

Author: Gilles Pisier
Title: The volume of convex bodies and Banach space geometry
Additional book information: Cambridge Tracts in Mathematics, vol. 94, Cambridge University Press, Cambridge, 1989, xv + 250 pp., $49.50. ISBN 0-521-364655.

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

  • S. Banach, Theory of linear operations, with a supplement by A. Pełczyński and C. Bessaga on Some aspects of the present theory of Banach spaces, North-Holland, Amsterdam, 1987. MR 880204
  • J. Bourgain and V. D. Milman, New volume ratio properties for convex symmetric bodies in R, Invent. Math. 88 (1987), 319-340. MR 880954
  • A. Dvoretzky, Some results on convex bodies and Banach spaces, Proceedings of the International Symposium on Linear Spaces held at the Hebrew University of Jerusalem, July 5-12, 1960, The Israel Academy of Sciences and Humanities, Jerusalem, 1961, pp. 123-160. MR 139079
  • T. Figiel, J. Lindenstrauss, and V. D. Milman, The dimension of almost spherical sections of convex bodies, Acta Math. 139 (1977), 53-94. MR 445274
  • Y. Gordon, Some inequalities for Gaussian processes and applications, Israel J. Math. 50 (1985), 265-289. MR 800188
  • Y. Gordon, Gaussian processes and almost spherical sections of convex bodies, Ann. Probab. 16 (1988), 180-188. MR 920263
  • F. John, Extremum problems with inequalities as subsidiary conditions, Studies and Essays presented to R. Courant on his 60th birthday, January 8, 1948, Interscience, New York, 1948, pp. 187-204. MR 30135
  • W. B. Johnson, H. König, B. Maurey, and J. R. Retherford, Eigenvalues of psumming and l, J. Funct. Anal. 32 (1979), 353-380. MR 538861
  • J. P. Kahane, Une inégalité du type de Slepian et Gordon sur les processus Gaussiens, Israel J. Math. 55 (1986), 109-110. MR 858463
  • B. Knaster, Problème 4, Colloq. Math. 1 (1947), 30-31.
  • K. Mahler, Ein Übertragungsprinzip für konvexe Körper, Časopis Pěst. Mat. 68 (1939), 93-102. MR 1242
  • B. Maurey and G. Pisier, Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach, Studia Math. 58 (1976), 45-90. MR 443015
  • M. Meyer and A. Pajor, On Santaló's inequality, GAFA Seminar, 1987-88, Lecture Notes in Math., vol. 1376, Springer-Verlag, Berlin and New York, 1989, pp. 261-263. MR 1008727
  • V. D. Milman, New proof of the theorem of Dvoretzky on sections of convex bodies, Funkcional Anal. i Prilozen 5 (1971), 28-37. (Russian) MR 293374
  • V. D. Milman, Almost Euclidean quotient spaces of subspaces of a finite-dimensional normed space, Proc. Amer. Math. Soc. 94 (1985), 445-449. MR 787891
  • V. D. Milman, Inégalité de Brunn-Minkowski inverse et applications à la théorie locale des espaces normés, C. R. Acad. Sci. Paris 302 (1986), 25-28. MR 827101
  • V. D. Milman, On a few observations on the connections between local theory and some other fields, GAFA Seminar, 1986-87, Lecture Notes in Math., vol. 1317, Springer-Verlag, Berlin and New York, 1988, pp. 283-289. MR 950988
  • G. Pisier, Holomorphic semi-groups and the geometry of Banach spaces, Ann. of Math. (2) 115 (1982), 375-392. MR 647811
  • G. Pisier, Weak Hilbert spaces, Proc. London Math. Soc. 56 (1988), 547-579. MR 931514
  • J. Saint-Raymond, Sur le volume des corps convexes symétriques, Séminaire Initiation à l'Analyse, 1980-81, Université P. et M. Curie, Paris, 1981. MR 670798
  • L. Santaló, Un invariante afin para los cuerpos convexos del espacio de n dimensions, Portugal. Math. 8 (1949), 155-161.

Review Information:

Reviewer: Donald L. Burkholder
Journal: Bull. Amer. Math. Soc. 25 (1991), 140-145
DOI: https://doi.org/10.1090/S0273-0979-1991-16046-5
American Mathematical Society