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Book Review

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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?)

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  • [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
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  • [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
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  • [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 $ {\mathcal {L}}_{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] V. D. Milman and G. 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] G. Pisier, The volume of convex bodies and Banach space geometry, Cambridge Tracts in Mathematics, vol. 94, Cambridge University Press, Cambridge, 1989. MR 1036275
  • [14] A. 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
Journal: Bull. Amer. Math. Soc. 54 (2017), 341-345
MSC (2010): Primary 52A21, 46B07, 52A23, 52A20
Published electronically: September 14, 2016
Review copyright: © Copyright 2016 American Mathematical Society
American Mathematical Society