Almost greedy uniformly bounded orthonormal bases in rearrangement invariant Banach function spaces (Q2891139)

Observing that in view of a result due to \textit{M. Nielsen} [J. Approx. Theory 149, No. 2, 188--192 (2007; Zbl 1146.46006)], 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. The purpose of this paper is to study these problems in the rearranged invariant Banach spaces. Thus the authors construct uniformly bounded orthogonal almost greedy bases in such spaces.