An example of an almost greedy uniformly bounded orthonormal basis for $L

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/119463We 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.8 pagesFunctional Analysis42C20An example of an almost greedy uniformly bounded orthonormal basis for $L_p([0,1])$text