Metric unconditionality and Fourier analysis

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dc.creatorNeuwirth, Stefan
dc.date1997-07-28
dc.date2001-04-23
dc.date.accessioned2026-07-07T09:08:27Z
dc.date.available2026-07-07T09:08:27Z
dc.descriptionWe investigate several aspects of almost 1-unconditionality. We characterize the metric unconditional approximation property UMAP in terms of ``block unconditionality''. Then we focus on translation invariant subspaces $L^p_E(T)$ and $C_E(T)$ of functions on the circle and express block unconditionality as arithmetical conditions on $E$. Our work shows that the spaces $L^p_E(T)$, $p$ an even integer, have a singular behaviour from the almost isometric point of view: property UMAP does not interpolate between spaces $L^p_E(T)$ and $L^{p+2}_E(T)$. These arithmetical conditions are used to construct counterexamples for several natural questions and to investigate the maximal density of such sets $E$. We also prove that if $E=\{n_k\}_{k\ge1}$ with $|n_{k+1}/n_k|\to\infty$, then $C_E(T)$ has UMAP and we get a sharp estimate of the Sidon constant of Hadamard sets. Finally, we investigate the relationship of metric unconditionality and probability theory.
dc.descriptionError in proof of Th. 8.3 (now 10.3.1) fixed. Ajout d'une introduction en francais
dc.identifierhttps://arxiv.org/abs/math/9707211
dc.identifierhttp://arxiv.org/abs/math/9707211
dc.identifierStudia Math. 131 (1998), no.1, pp.19--62
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/150723
dc.subjectFunctional Analysis
dc.subject42A55, 46B28, 46B04
dc.titleMetric unconditionality and Fourier analysis
dc.typetext

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