Embedding subspaces of 𝑙ⁿ_{∞} into spaces with Schauder basis

Mankiewicz, Piotr; Tomczak-Jaegermann, Nicole

doi:10.1090/S0002-9939-1993-1143019-4

Embedding subspaces of $l^ n_ \infty$ into spaces with Schauder basis
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by Piotr Mankiewicz and Nicole Tomczak-Jaegermann PDF

Proc. Amer. Math. Soc. 117 (1993), 459-465 Request permission

Abstract:

It is proved that for sufficiently small $\varepsilon > 0$ and any $0 < \delta < 1/2$, a random $n$-dimensional subspace $E$ of $l_\infty ^N$, where $N = (1 + \varepsilon )n$, has the property: whenever $E$ is embedded into any $(1 + \gamma )n$-dimensional space with a basis, where $\gamma = c\delta \varepsilon$, then the embedding constant exceeds ${c’}{n^{1/2 - \delta }}$.

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