An example of an almost greedy uniformly bounded orthonormal basis for $L_p([0,1])$

Morten Nielsen

An example of an almost greedy uniformly bounded orthonormal basis for $L_p([0,1])$

Functional Analysis 2007-05-23 v1

Authors: Morten Nielsen

Abstract

We construct a uniformly bounded orthonormal almost greedy basis for $L_p([0,1])$ , $1<p<\infty$ . The example shows that it is not possible to extend Orlicz's theorem, stating that there are no uniformly bounded orthonormal unconditional bases for $L_p([0,1])$ , $p\not=2$ , to the class of almost greedy bases.

Keywords

almost greedy basis uniformly bounded orthonormal basis lp space orlicz theorem unconditional basis

Cite

@article{arxiv.math/0611890,
  title  = {An example of an almost greedy uniformly bounded orthonormal basis for $L_p([0,1])$},
  author = {Morten Nielsen},
  journal= {arXiv preprint arXiv:math/0611890},
  year   = {2007}
}

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8 pages

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