Quotients of finite-dimensional quasi-normed spaces

Details Quotients of finite-dimensional quasi-normed spaces Quotients of finite-dimensional quasi-normed spaces

2001-04-11

arxiv.org/abs/math/0104120v1

Mathematics

Functional Analysis

13 pages

Scientific paper

We study the existence of cubic quotients of finite-dimensional quasi-normed spaces, that is, quotients well isomorphic to $\ell_{\infty}^k$ for some $k.$ We give two results of this nature. The first guarantees a proportional dimensional cubic quotient when the envelope is cubic; the second gives an estimate for the size of a cubic quotient in terms of a measure of non-convexity of the quasi-norm.

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