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
Somaglia, J
2021-01-01
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.File in questo prodotto:
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Russo, Somaglia - Overcomplete sets in non-separable Banach spaces.pdf
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