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- W4300520817 abstract "A generalization of Lozanovskii's result is proved. Let E be $k$-dimensional subspace of an $n$-dimensional Banach space with unconditional basis. Then there exist $x_1,..,x_k subset E$ such that $B_E p subset p absconv{x_1,..,x_k}$ and [ kla frac{{rm vol}(absconv{x_1,..,x_k})}{{rm vol}(B_E)} mer^{frac{1}{k}} kl kla ep frac{n}{k} mer^2 pl .] This answers a question of V. Milman which appeared during a GAFA seminar talk about the hyperplane problem. We add logarithmical estimates concerning the hyperplane conjecture for proportional subspaces and quotients of Banach spaces with unconditional basis. File Length:27K" @default.
- W4300520817 created "2022-10-03" @default.
- W4300520817 creator A5030843204 @default.
- W4300520817 date "1993-12-29" @default.
- W4300520817 modified "2023-10-16" @default.
- W4300520817 title "Proportional subspaces of spaces with unconditional basis have good volume properties" @default.
- W4300520817 doi "https://doi.org/10.48550/arxiv.math/9312208" @default.
- W4300520817 hasPublicationYear "1993" @default.
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