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.
Overcomplete sets in non-separable Banach spaces / T. Russo, J. Somaglia. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - 149:2(2021 Feb), pp. 701-714. [10.1090/proc/15213]
Overcomplete sets in non-separable Banach spaces
J. SomagliaSecondo
2021
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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