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On Dvoretzky’s theorem on almost spherical sections of convex bodies. (English) Zbl 0288.52002


MSC:

52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
52A40 Inequalities and extremum problems involving convexity in convex geometry
46B99 Normed linear spaces and Banach spaces; Banach lattices
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References:

[1] A. Dvoretzky,Some results on convex bodies and Banach spaces, Proc. Symp. on Linear Spaces, Jerusalem, 1961. · Zbl 0119.31803
[2] Figiel, T., Some remarks on Dvoretzky’s theorem on almost spherical sections of convex bodies, Coll. Math., 24, 241-252 (1972) · Zbl 0244.28011
[3] James, R. C., Uniformly non-square Banach spaces, Ann. of Math., 80, 542-550 (1964) · Zbl 0132.08902
[4] Lindenstrauss, J.; Pełczyński, A., Contributions to the theory of the classical Banach spaces, J. Functional Anal., 8, 225-249 (1971) · Zbl 0224.46041
[5] J. Lindenstrauss and L. Tzafriri,Classical Banach Spaces, Lecture Notes in Math. No. 338, Springer-Verlag, 1973. · Zbl 0259.46011
[6] V. D. Milman,New proof of the theorem of A. Dvoretzky on intersections of convex bodies, Functional. Anal. i Priložen.5 (1971), (Russian); English transl., Functional Anal. Appl., 288-295. · Zbl 0239.46018
[7] Milman, V. D., The geometric theory of Banach spaces, Part II, Uspehi Mat. Nauk., 26, 73-149 (1971) · Zbl 0229.46017
[8] Tzafriri, L., On Banach spaces with unconditional bases, Israel J. Math., 17, 84-92 (1974) · Zbl 0281.46013
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