×

zbMATH — the first resource for mathematics

A quantitative finite-dimensional Krivine theorem. (English) Zbl 0612.46021
From the authors’ abstract: Measure concentration arguments are applied to get a power-type estimate for the dimension of almost \(\ell_ p\) subspaces of isomorphs of \(\ell^ n_ p\) and for the length of almost- symmetric sequences under a nonlinear-type condition.
Reviewer: A.J.Ellis

MSC:
46B25 Classical Banach spaces in the general theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] N. Alon and D. Milman,Embedding of l k in finite dimensional Banach spaces, Isr. J. Math.45 (1983), 265–280. · Zbl 0546.46015
[2] D. Amir and V. D. Milman,Unconditional and symmetric sets in n-dimensional normed spaces, Isr. J. Math.37 (1980), 3–20. · Zbl 0445.46011
[3] T. Figiel, J. Lindenstrauss and V. D. Milman,The dimensions of almost spherical sections of convex bodies, Acta Math.139 (1977), 53–94. · Zbl 0375.52002
[4] M. Gromov and V. D. Milman,A topological application of the isoperimetric inequality, Am. J. Math.105 (1983), 843–854. · Zbl 0522.53039
[5] M. Gromov and V. D. Milman,Brunn theorem and a concentration of volume phenomena for symmetric convex bodies, Geometrical Aspects of Functional Analysis, Seminar Notes, Tel Aviv, 1983–4.
[6] V. I. Gurari, M. I. Kadec and V. I. Macaev,On Banach-Mazur distance between certain Minkowski spaces, Bull. Acad. Polon. Sci.13 (1965), 719–722.
[7] J. L. Krivine,Sous espaces de dimension finis des espaces de Banach reticulés, Ann. of Math.104 (1976), 1–29. · Zbl 0329.46008
[8] D. R. Lewis,Finite dimensional subspaces of L p, Studia Math.63 (1978), 207–212. · Zbl 0406.46023
[9] B. Maurey,Construction de suites symétriques, Comptes Rendus Acad. Sci. Paris.288 (1979), A679-A681. · Zbl 0398.46019
[10] V. D. Milman,A new proof of the theorem of A. Dvoretzky on sections of convex bodies, Funct. Anal. Appl.5 (1971), 28–37 (transl. from Russian).
[11] V. D. Milman and G. Schechtman,Asymptotic Theory of Finite Dimensional Banach Spaces, Springer Lecture Notes, to appear. · Zbl 0911.52002
[12] G. Pisier,On the dimension of the l p n -subspaces of Banach spaces, for 1<2, Trans. Am. Math. Soc.276 (1983), 201–211. · Zbl 0509.46016
[13] G. Schechtman,Levy type inequality for a class of finite metric spaces, inMartingale Theory in Harmonic Analysis and Applications, Cleveland 1981, Springer Lecture Notes in Math. No. 939, 1982, pp. 211–215.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.