This is an announcement for the paper “Overcomplete sets in Banach spaces” by Tommaso Russohttps://arxiv.org/search/math?searchtype=author&query=Russo%2C+T, Jacopo Somagliahttps://arxiv.org/search/math?searchtype=author&query=Somaglia%2C+J.

Abstract: We introduce and study the notion of overcomplete set in a Banach space, that subsumes and extends the classical concept of overcomplete sequence in a (separable) Banach space. We give existence and non-existence results of overcomplete sets for a wide class of (non-separable) Banach spaces and we study to which extent properties of overcomplete sequences are retained by every overcomplete set.

https://arxiv.org/abs/1912.08690