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

Morten Nielsen

paper

An example of an almost greedy uniformly bounded orthonormal basis for $L_{p} ([0, 1])$

arXiv:math/0611890

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 $L_{p} ([0, 1])$ , $p \neq = 2$ , to the class of almost greedy bases.

8 pages

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

Abstract

An example of an almost greedy uniformly bounded orthonormal basis for $L_{p} ([0, 1])$