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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Embedding subspaces of $ l\sp n\sb \infty$ into spaces with Schauder basis


Authors: Piotr Mankiewicz and Nicole Tomczak-Jaegermann
Journal: Proc. Amer. Math. Soc. 117 (1993), 459-465
MSC: Primary 46B20; Secondary 46B15
MathSciNet review: 1143019
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1143019-4
PII: S 0002-9939(1993)1143019-4
Article copyright: © Copyright 1993 American Mathematical Society