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References
Bohnenblust, F., Subspaces ofl p,n spaces.Amer. J. Math., 63 (1941), 64–72.
Chevet, S., Series de variables aleatoires gaussiennes a valeurs dansE⊗ɛ F.Séminaire sur la geometrie des espaces de Banach 1977–78, Exposé No. XIX, École Polytechnique, Palaiseau.
Enflo, P., A counterexample to the approximation property in Banach spaces.Acta Math., 130 (1973), 309–317.
Figiel, T., Kwapień, S., Pełczyński, A., Sharp estimates for the constants of local unconditional structure for Minkowski spaces.Bull. Acad. Polon. Sci., 25 (1977), 1221–1226.
Gluskin, E. D., The diameter of the Minkowski compactum is roughly equal ton. Functional Anal. Appl., 15 (1981), 72–73.
Gluskin, E. D., Finite dimensional analogues of spaces without a basis.Dokl. Akad. Nauk SSSR. To appear.
Gordon, Y. &Lewis, D. R., Absolutely summing operators and local unconditional structures.Acta Math., 133 (1974), 27–48.
Helgason, S.,Differential Geometry, Lie Groups and Symmetric Spaces. Academic Press, 1978.
Kashin, B. S., Sections of some finite dimensional sets and classes of smooth functions,Izv. Akad. Nauk SSSR, Ser. Mat., 41 (1977), 334–351. (russian).
Kisliakov, S. V., PreprintLOMI 6-80. Leningrad 1980.
—, On Spaces with “small” annihilators.Zap. Naučn. Sem. LOMI, 65 (1978), 192–195 (russian).
Lewis, D. R., Finite dimensional subspaces ofL p .,Studia Math., 63 (1978), 207–212.
Lindenstrauss, J. & Tzafriri, L.,Classical Banach Spaces I. Springer-Verlag, 1977.
Pisier, G., Une nouvelle classe d'espaces vérifiant le théorème de Grothendieck.Ann. Inst. Fourier, 28 (1978), 69–90.
Pisier, G., A remark on certain quotients of Banach spaces of cotypeq. École Polytechnique, Palaiseau, March 1981. Preprint.
Pisier, G. Counterexamples to a conjecture of Grothendieck. To appear.
Szarek, S. J., On Kashin's almost orthogonal decomposition ofl 1 n .Bull. Acad. Polon. Sci., 26 (1978), 691–694.
Szarek, S. J., Volume estimates and nearly Euclidean decompositions of normed spaces.Séminaire d'Analyse Fonctionnelle 1979–80, Exposé No XXV, École Polytechnique, Palaiseau.
Szarek, S. J., Nets of Grassmann manifold and orthogonal group.Proceedings of Banach Space Workshop, University of Iowa Press 1981.
Szarek, S. J. &Tomczak-Jaegermann, N., On nearly Euclidean decomposition for some classes of Banach spaces,Compositio Math., 40 (1980), 367–385.
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Szarek, S.J. The finite dimensional basis problem with an appendix on nets of Grassmann manifolds. Acta Math. 151, 153–179 (1983). https://doi.org/10.1007/BF02393205
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DOI: https://doi.org/10.1007/BF02393205