Abstract
We extend the results of [LMT] to the non-symmetric and quasi-convex cases. Namely, we consider a finite-dimensional space endowed with the gauge of either a closed convex body (not necessarily symmetric) or a closed symmetric quasi-convex body. We show that if a generic subspace of some fixed proportional dimension of one such space is isomorphic to a generic quotient of some proportional dimension of another space then for any proportion arbitrarily close to 1, the first space has a lot of Euclidean subspaces and the second space has a lot of Euclidean quotients.
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© 2004 Springer-Verlag Berlin/Heidelberg
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Litvak, A.E., Milman, V.D., Tomczak-Jaegermann, N. (2004). Isomorphic Random Subspaces and Quotients of Convex and Quasi-Convex Bodies. In: Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 1850. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44489-3_15
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DOI: https://doi.org/10.1007/978-3-540-44489-3_15
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22360-3
Online ISBN: 978-3-540-44489-3
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