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.
@article{bwmeta1.element.bwnjournal-article-smv112i1p59bwm,
author = {J\"org Wenzel},
title = {Ideal norms and trigonometric orthonormal systems},
journal = {Studia Mathematica},
volume = {108},
year = {1994},
pages = {59-74},
zbl = {0824.46012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv112i1p59bwm}
}
Wenzel, Jörg. Ideal norms and trigonometric orthonormal systems. Studia Mathematica, Tome 108 (1994) pp. 59-74. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv112i1p59bwm/
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