A note on partially-greedy bases in quasi-Banach spaces
Volume 259 / 2021
Studia Mathematica 259 (2021), 225-239 MSC: 46B15, 41A65. DOI: 10.4064/sm200402-20-8 Published online: 7 January 2021
We continue the study of greedy-type bases in quasi-Banach spaces started by Albiac et al. [arXiv:1903.11651]. In the present paper, we study partially-greedy bases, focusing on two main results:
$\bullet$ Characterization of partially-greedy bases in quasi-Banach spaces in terms of quasi-greediness and various conservative-like properties.
$\bullet$ Given a $C$-partially-greedy basis in a quasi-Banach space, there exists a “renorming” such that the basis is $1$-partially-greedy.