Geodesic
Ideal norms and trigonometric orthonormal systems
Studia Mathematica, Tome 112 (1994) no. 1, pp. 59-74

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DOI

We characterize the UMD-property of a Banach space X by sequences of ideal norms associated with trigonometric orthonormal systems. The asymptotic behavior of those numerical parameters can be used to decide whether X is a UMD-space. Moreover, if this is not the case, we obtain a measure that shows how far X is from being a UMD-space. The main result is that all described sequences are not only simultaneously bounded but are also asymptotically equivalent. 
Jörg Wenzel. Ideal norms and trigonometric orthonormal systems. Studia Mathematica, Tome 112 (1994) no. 1, pp. 59-74. doi: 10.4064/sm-112-1-59-74
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