Non-equivalent greedy and almost greedy bases in \(\ell_p\) (Q2369470)

Summary: For \(1 < p < \infty\) and \(p\neq 2\), we construct a family of mutually non-equivalent greedy bases in \(\ell_p\) having the cardinality of the continuum. In fact, no basis from this family is equivalent to a rearranged subsequence of any other basis thereof. We are able to extend this statement to the spaces \(L_p\) and \(H_1\). Moreover, the technique used in the proof adapts to the setting of almost greedy bases where similar results are obtained.