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1985•Proceedings of the American Mathematical SocietyOpen access

Almost Euclidean Quotient Spaces of Subspaces of a Finite-Dimensional Normed Space

Vitali Davidovich Milman

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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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What this paper is about

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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OpenAlex reports 10 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available 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).

Key concepts: Quotient space (topology), Normed vector space, Linear subspace, Mathematics, Quotient, Space (punctuation), Euclidean space, Lambda

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