Overcomplete sets in non-separable Banach spaces

Russo, Tommaso; Somaglia, Jacopo

doi:10.1090/proc/15213

Overcomplete sets in non-separable Banach spaces
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by Tommaso Russo and Jacopo Somaglia PDF

Proc. Amer. Math. Soc. 149 (2021), 701-714 Request permission

Abstract:

We introduce and study the notion of overcomplete sets 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.

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