Random sign embeddings from 𝑙ⁿᵣ,2<𝑟<∞

Figiel, T.; Johnson, W. B.; Schechtman, G.

doi:10.1090/S0002-9939-1988-0915724-1

Random sign embeddings from $l^n_r,\;2 < r < \infty$

Authors: T. Figiel, W. B. Johnson and G. Schechtman
Journal: Proc. Amer. Math. Soc. 102 (1988), 102-106
MSC: Primary 46B25,; Secondary 47B10,47B37,47D30
DOI: https://doi.org/10.1090/S0002-9939-1988-0915724-1
MathSciNet review: 915724
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Abstract: Estimates for any ideal norm of a "random sign embedding" from $l_r^n$ into $l_r^m,\;2 < r < \infty$, are given in terms of the corresponding ideal norm of the identity of $l_r^k,\;k = k(n,m,r)$.

G. Bennett, L. E. Dor, V. Goodman, W. B. Johnson, and C. M. Newman, On uncomplemented subspaces of $L_{p},$ $1<p<2$, Israel J. Math. 26 (1977), no. 2, 178–187. MR 435822, DOI https://doi.org/10.1007/BF03007667
Chong-Man Cho and William B. Johnson, $M$-ideals and ideals in $L(X)$, J. Operator Theory 16 (1986), no. 2, 245–260. MR 860345
John Elton, Sign-embeddings of $l^{n}_{1}$, Trans. Amer. Math. Soc. 279 (1983), no. 1, 113–124. MR 704605, DOI https://doi.org/10.1090/S0002-9947-1983-0704605-4
T. Figiel, J. Lindenstrauss, and V. D. Milman, The dimension of almost spherical sections of convex bodies, Acta Math. 139 (1977), no. 1-2, 53–94. MR 445274, DOI https://doi.org/10.1007/BF02392234
E. D. Gluskin, A. Pietsch, and J. Puhl, A generalization of Khintchine’s inequality and its application in the theory of operator ideals, Studia Math. 67 (1980), no. 2, 149–155. MR 583295, DOI https://doi.org/10.4064/sm-67-2-149-155
W. B. Johnson, B. Maurey, G. Schechtman, and L. Tzafriri, Symmetric structures in Banach spaces, Mem. Amer. Math. Soc. 19 (1979), no. 217, v+298. MR 527010, DOI https://doi.org/10.1090/memo/0217
W. B. Johnson and G. Schechtman, On subspaces of $L_{1}$ with maximal distances to Euclidean space, Proceedings of research workshop on Banach space theory (Iowa City, Iowa, 1981) Univ. Iowa, Iowa City, IA, 1982, pp. 83–96. MR 724107
Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. I, Springer-Verlag, Berlin-New York, 1977. Sequence spaces; Ergebnisse der Mathematik und ihrer Grenzgebiete, Vol. 92. MR 0500056
Alain Pajor, Plongement de $l^{n}_{1}$ dans les espaces de Banach complexes, C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), no. 17, 741–743 (French, with English summary). MR 707332
Albrecht Pietsch, Operator ideals, North-Holland Mathematical Library, vol. 20, North-Holland Publishing Co., Amsterdam-New York, 1980. Translated from German by the author. MR 582655

---, Rosenthal’s inequality and its application in the theory of operator ideals, Proc. Internat. Conf. Operator Algebras, Ideals, ..., Teubner-Texte zur Math., Leipzig, 1978, pp. 80-88.

Haskell P. Rosenthal, On the subspaces of $L^{p}$ $(p>2)$ spanned by sequences of independent random variables, Israel J. Math. 8 (1970), 273–303. MR 271721, DOI https://doi.org/10.1007/BF02771562
Nicole Tomczak-Jaegermann, The weak distance between finite-dimensional Banach spaces, Math. Nachr. 119 (1984), 291–307. MR 774197, DOI https://doi.org/10.1002/mana.19841190126