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Almost Euclidean quotient spaces of subspaces of a finite-dimensional normed space


Author: V. D. Milman
Journal: Proc. Amer. Math. Soc. 94 (1985), 445-449
MSC: Primary 46B20
DOI: https://doi.org/10.1090/S0002-9939-1985-0787891-1
MathSciNet review: 787891
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Abstract: The main result of this article is Theorem 1 which states that a quotient space $ Y,\dim Y = k$, of a subspace of any finite dimensional normed space $ X$, may be chosen to be $ d$-isomorphic to a euclidean space even for $ k = [\lambda n]$ for any fixed $ \lambda < 1$ (and $ d$ depending on $ \lambda $ only).


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0787891-1
Keywords: Finite-dimensional spaces, euclidean spaces
Article copyright: © Copyright 1985 American Mathematical Society

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