  We introduce and study the notion of weak weight-semi-greedy Markushevich
bases - which extends the concepts of weight semi-greedy and weak semi-greedy
Markushevich bases. In particular, we study conditions under which such bases
are weight almost greedy. We also define the notion of weak weight almost
greedy bases, and prove that this formally weaker concept is equivalent to that
concept of weight almost greedy bases. Finally, we study some parameters
involving the weak thresholding and Chebyshevian greedy algorithms.
