Special orthogonal splittings of \(L_1^{2k}\)

DOI10.1007/BF02787555zbMath1066.46010arXivmath/0301275MaRDI QIDQ1885599

Gideon Schechtman

Publication date: 11 November 2004

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0301275

zbMATH Keywords

orthogonal decompositionKashin splittingrandom \(\pm 1\) matrixuniversally equivalent norms

Mathematics Subject Classification ID

Local theory of Banach spaces (46B07) Probabilistic methods in Banach space theory (46B09) Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21)

Related Items

Random Euclidean embeddings in spaces of bounded volume ratio, Singularity of discrete random matrices, Diameters of sections and coverings of convex bodies, Sparsity and non-Euclidean embeddings, Subspaces and orthogonal decompositions generated by bounded orthogonal systems, Random embedding of \({\ell_p^n}\) into \({\ell_r^N}\), Explicit Euclidean embeddings in permutation invariant normed spaces, The smallest singular value of a shifted $d$-regular random square matrix, Weak Grothendieck's theorem, Polynomial bounds for large Bernoulli sections of \(\ell_1^N\), Logarithmic reduction of the level of randomness in some probabilistic geometric constructions, Three-space problems for the approximation property

Cites Work

• Unnamed Item
• Asymptotic theory of finite dimensional normed spaces. With an appendix by M. Gromov: Isoperimetric inequalities in Riemannian manifolds
• Random embeddings of Euclidean spaces in sequence spaces
• The dimension of almost spherical sections of convex bodies
• Very tight embeddings of subspaces of \(L_p\), \(1 \leq p < 2\), into \(\ell^n_p\)
• Integral Kašin splittings
• An Isoperimetric Theorem on the Cube and the Kintchine-Kahane Inequalities
• On the best constants in the Khinchin inequality