On the size of the set of unbounded multilinear operators between Banach spaces

On the size of the set of unbounded multilinear operators between Banach spaces

Among other results we investigate (α,β)-lineability of the set of non-continuous m-linear operators defined between normed spaces as a subset of the space of all m-linear operators. We also give a partial answer to an open problem on the lineability of the set of non absolutely summing operators.

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Veröffentlicht in:Linear algebra and its applications 2020-12, Vol.606, p.144-158
Hauptverfasser: Fávaro, V.V., Pellegrino, D.M., Rueda, P.
Format: Artikel
Sprache:eng
Schlagworte:
Banach spaces
Lineability
Linear algebra
Linear operators
Multilinear operators
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Zusammenfassung:Among other results we investigate (α,β)-lineability of the set of non-continuous m-linear operators defined between normed spaces as a subset of the space of all m-linear operators. We also give a partial answer to an open problem on the lineability of the set of non absolutely summing operators.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2020.07.029