On consecutive greedy and other greedy-like type of bases

We continue our study of the thresholding greedy algorithm when we restrict the vectors involved in our approximations so that they either are supported on intervals of \(\mathbb {N}\) $\mathbb{N}$ or have constant coefficients. We introduce and characterize what we call consecutive greedy bases and provide new characterizations of almost greedy and squeeze symmetric Schauder bases. Moreover, we investigate some cases involving greedy-like properties with constant 1 and study the related notion of Property (A, \(\tau \) $\tau$ ).