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Ideal norms and trigonometric orthonormal systems

Joerg Wenzel
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Abstract

In this article, we characterize the $UMD$--property of a Banach space $X$ by ideal norms associated with trigonometric orthonormal systems. The asymptotic behavior of that numerical parameters can be used to decide whether or not $X$ is a $UMD$--space. Moreover, in the negative case, we obtain a measure that shows how far $X$ is from being a $UMD$--space. The main result is, that all described parameters are equivalent also in the quantitative setting.

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Joerg Wenzel. 1994-04-12. Ideal norms and trigonometric orthonormal systems. https://arxiv.org/abs/math/9404208

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