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Ideal norms and trigonometric orthonormal systems

100%

Wenzel J.

Studia Mathematica

1994-1995

tom 112

nr 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.

On the non-equivalence of rearranged Walsh and trigonometric systems in $L_{p}$

63%

Hinrichs A., Wenzel J.

Studia Mathematica

2003

tom 159

nr 3

435-451

We consider the question of whether the trigonometric system can be equivalent to some rearrangement of the Walsh system in $L_{p}$ for some p ≠ 2. We show that this question is closely related to a combinatorial problem. This enables us to prove non-equivalence for a number of rearrangements. Previously this was known for the Walsh-Paley order only.

Ograniczanie wyników

2 Studia Mathematica

2 Wenzel J.

1 Hinrichs A.

1 2003

1 1994

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Ideal norms and trigonometric orthonormal systems

On the non-equivalence of rearranged Walsh and trigonometric systems in $L_{p}$