Non-equivalent greedy and almost greedy bases in lp

Abstract

For 1 < p < 8 and p ? 2 we construct a family of mutually non-equivalent greedy bases in lp 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 Lp and H₁. Moreover, the technique used in the proof adapts to the setting of almost greedy bases where similar results are obtained.