[S]-linear and convex structures in function families

In this paper, the notion of [S]-lineability (originally coined by Vladimir I. Gurariy) is introduced and developed in a general abstract setting. This new notion is, then, applied to specific situations, as for instance, classes of differentiable nowhere monotone functions as well as families of ve...

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Bibliographic Details
Published in:Linear algebra and its applications 2019-10, Vol.579, p.463-483
Main Authors: Bernal-González, L., Conejero, J.A., Murillo-Arcila, M., Seoane-Sepúlveda, J.B.
Format: Article
Language:English
Subjects:
Convexity
Hypercyclic operator
Köthe space
Lineability
Mixing map
Spaceability
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Summary:In this paper, the notion of [S]-lineability (originally coined by Vladimir I. Gurariy) is introduced and developed in a general abstract setting. This new notion is, then, applied to specific situations, as for instance, classes of differentiable nowhere monotone functions as well as families of vectors having dense orbit with respect to an operator. Large convex structures are also shown to exist inside the family of topologically mixing continuous selfmaps of a real compact interval.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2019.07.003