Existence and uniqueness of greedy bases in Banach spaces

Abstract

Our aim is to investigate the properties of existence and uniqueness of greedy bases in Banach spaces. We show the non-existence of greedy basis in some Nakano spaces and Orlicz sequence spaces and produce the first-known examples of non-trivial spaces (i.e., different from $c_0$, ${\ell }_1$, and ${\ell }_2$) with a unique greedy basis.