# Ideal norms and trigonometric orthonormal systems

Studia Mathematica (1994)

- Volume: 112, Issue: 1, page 59-74
- ISSN: 0039-3223

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topWenzel, Jörg. "Ideal norms and trigonometric orthonormal systems." Studia Mathematica 112.1 (1994): 59-74. <http://eudml.org/doc/216137>.

@article{Wenzel1994,

abstract = {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.},

author = {Wenzel, Jörg},

journal = {Studia Mathematica},

keywords = {UMD-property; trigonometric orthonormal systems; asymptotically equivalent},

language = {eng},

number = {1},

pages = {59-74},

title = {Ideal norms and trigonometric orthonormal systems},

url = {http://eudml.org/doc/216137},

volume = {112},

year = {1994},

}

TY - JOUR

AU - Wenzel, Jörg

TI - Ideal norms and trigonometric orthonormal systems

JO - Studia Mathematica

PY - 1994

VL - 112

IS - 1

SP - 59

EP - 74

AB - 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.

LA - eng

KW - UMD-property; trigonometric orthonormal systems; asymptotically equivalent

UR - http://eudml.org/doc/216137

ER -

## References

top- [1] J. Bourgain, Some remarks on Banach spaces in which martingale difference sequences are unconditional, Ark. Mat. 22 (1983), 163-168. Zbl0533.46008
- [2] D. L. Burkholder, Martingales and Fourier analysis in Banach spaces, in: Probability and Analysis (Varenna, Italy, 1985), Lecture Notes in Math. 1206, Springer, 1986, 61-108.
- [3] M. Defant, Zur vektorwertigen Hilberttransformation, Ph.D. thesis, Christian-Albrechts-Universität Kiel, 1986. Zbl0614.46060
- [4] N. Dinculeanu, Vector Measures, Deutscher Verlag der Wiss., Berlin, 1966.
- [5] A. Pietsch, Operator Ideals, Deutscher Verlag der Wiss., Berlin, 1978.
- [6] A. Pietsch, Eigenvalues and s-numbers, Akademische Verlagsgesellschaft Geest & Portig K.-G., Leipzig, 1987. Zbl0615.47019
- [7] A. Pietsch and J. Wenzel, Orthogonal systems and geometry of Banach spaces, in preparation. Zbl0919.46001
- [8] A. Zygmund, Trigonometric Series, 2nd ed., Cambridge University Press, Cambridge, 1959. Zbl0085.05601

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