Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF
Book Information:

Authors: Shiri Artstein-Avidan, Apostolos Giannopoulos and Vitali D. Milman
Title: Asymptotic geometric analysis, Part I
Additional book information: Mathematical Surveys and Monographs, Vol. 202, American Mathematical Society, Providence, RI, 2015, xx+451 pp., ISBN 978-1-4704-2193-9

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

  • [1] Stefan Banach, Théorie des opérations linéaires, Chelsea Publishing Co., New York, 1955 (French). MR 0071726
  • [2] Silouanos Brazitikos, Apostolos Giannopoulos, Petros Valettas, and Beatrice-Helen Vritsiou, Geometry of isotropic convex bodies, Mathematical Surveys and Monographs, vol. 196, American Mathematical Society, Providence, RI, 2014. MR 3185453
  • [3] Aryeh Dvoretzky, Some results on convex bodies and Banach spaces, Proc. Internat. Sympos. Linear Spaces (Jerusalem, 1960) Jerusalem Academic Press, Jerusalem; Pergamon, Oxford, 1961, pp. 123–160. MR 0139079
  • [4] A. Dvoretzky and C. A. Rogers, Absolute and unconditional convergence in normed linear spaces, Proc. Nat. Acad. Sci. U. S. A. 36 (1950), 192–197. MR 0033975
  • [5] T. Figiel, A short proof of Dvoretzky’s theorem, Séminaire Maurey-Schwartz 1974–1975: Espaces 𝐿^{𝑝}, applications radonifiantes et géométrie des espaces de Banach, Exp. No. XXIII, Centre Math., École Polytech., Paris, 1975, pp. 6 pp. (erratum, p. 3). MR 0407566
  • [6] A. Grothendieck, Résumé des résultats essentiels dans la théorie des produits tensoriels topologiques et des espaces nucléaires, Ann. Inst. Fourier Grenoble 4 (1952), 73–112 (1954) (French). MR 0061754
  • [7] A. Grothendieck, Sur certaines classes de suites dans les espaces de Banach et le théorème de Dvoretzky-Rogers, Bol. Soc. Mat. São Paulo 8 (1953), 81–110 (1956) (French). MR 0094683
  • [8] Paul Lévy, Problèmes concrets d’analyse fonctionnelle. Avec un complément sur les fonctionnelles analytiques par F. Pellegrino, Gauthier-Villars, Paris, 1951 (French). 2d ed. MR 0041346
  • [9] J. Lindenstrauss and A. Pełczyński, Absolutely summing operators in 𝐿_{𝑝}-spaces and their applications, Studia Math. 29 (1968), 275–326. MR 0231188
  • [10] J. Lindenstrauss and H. P. Rosenthal, The \cal𝐿_{𝑝} spaces, Israel J. Math. 7 (1969), 325–349. MR 0270119
  • [11] V. D. Milman, A new proof of A. Dvoretzky’s theorem on cross-sections of convex bodies, Funkcional. Anal. i Priložen. 5 (1971), no. 4, 28–37 (Russian). MR 0293374
  • [12] Vitali D. Milman and Gideon Schechtman, Asymptotic theory of finite-dimensional normed spaces, Lecture Notes in Mathematics, vol. 1200, Springer-Verlag, Berlin, 1986. With an appendix by M. Gromov. MR 856576
  • [13] Gilles Pisier, The volume of convex bodies and Banach space geometry, Cambridge Tracts in Mathematics, vol. 94, Cambridge University Press, Cambridge, 1989. MR 1036275
  • [14] Andrzej Szankowski, On Dvoretzky’s theorem on almost spherical sections of convex bodies, Israel J. Math. 17 (1974), 325–338. MR 0350388
  • [15] L. Tzafriri, On Banach spaces with unconditional bases, Israel J. Math. 17 (1974), 84–93. MR 0348456

Review Information:

Reviewer: Gideon Schechtman
Affiliation: Department of Mathematics Weizmann Institute of Science Rehovot, Israel
Email: gideon@weizmann.ac.il
Journal: Bull. Amer. Math. Soc.
DOI: https://doi.org/10.1090/bull/1558
Published electronically: September 14, 2016
Review copyright: © Copyright 2016 American Mathematical Society