Ideal norms and trigonometric orthonormal systems
Volume 112 / 1994
Studia Mathematica 112 (1994), 59-74 DOI: 10.4064/sm-112-1-59-74
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.