Weak semi-greedy bases and the equivalence between semi-greedy, branch semi-greedy, and almost greedy Markushevich bases in Banach spaces

BERASATEGUI, MIGUEL; LASSALLE, SILVIA

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS

BIRKHAUSER BOSTON INC

Año: 2021

1069-5869

We introduce and study the notion of weak semi-greedy systems -which is inspired in the concepts of semi-greedy and branch semi-greedy systems and weak thresholding sets-, and prove that in infinite dimensional Banach spaces, the notions of extit{ semi-greedy, branch semi-greedy, weak semi-greedy, and almost greedy} Markushevich bases are all equivalent. This completes and extends some results from (Berna2019), (Dilworth et al 2003), and (Dilworth et a 2012). We also exhibit an example of a semi-greedy system that is neither almost greedy nor a Markushevich basis, showing that the Markushevich condition cannot be dropped from the equivalence result. In some cases, we obtain improved upper bounds for the corresponding constants of the systems.