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