Characterization of [formula omitted]-quasi-greedy bases.

In this note we continue the study initiated in Albiac and Wojtaszczyk (2006) of greedy-like bases in the “isometric case”, i.e., in the case that the constants that arise in the context of greedy bases in their different forms are 1 . Here we settle the problem to find a satisfactory characterization of 1 -quasi-greedy bases in Banach spaces. We show that a semi-normalized basis in a Banach space is quasi-greedy with quasi-greedy constant 1 if and only if it is unconditional with suppression-unconditional constant 1 . [ABSTRACT FROM AUTHOR]