Spaceability of sets of non-injective maps
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909168925933568 |
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| author | Aires, Mikaela Botelho, Geraldo |
| author_facet | Aires, Mikaela Botelho, Geraldo |
| contents | Generalizing a recent result on lineability of sets of non-injective linear operators, we prove, for quite general linear spaces $A$ of maps from an arbitraty set to a sequence space, that, for every $0 \neq f \in A$, the subset of $A$ of non-injective maps contains an infinite dimensional subspace of $A$ containing $f$. We provide aplications of the main result to spaces of linear operators between quasi-Banach spaces, to spaces of linear operators belonging to an operator ideal, and, in the nonlinear setting, to linear spaces of homogeneous polynomials and to linear spaces of vector-valued Lispshitz functions on metric spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19855 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spaceability of sets of non-injective maps Aires, Mikaela Botelho, Geraldo Functional Analysis 15A03, 46B87, 47B10 Generalizing a recent result on lineability of sets of non-injective linear operators, we prove, for quite general linear spaces $A$ of maps from an arbitraty set to a sequence space, that, for every $0 \neq f \in A$, the subset of $A$ of non-injective maps contains an infinite dimensional subspace of $A$ containing $f$. We provide aplications of the main result to spaces of linear operators between quasi-Banach spaces, to spaces of linear operators belonging to an operator ideal, and, in the nonlinear setting, to linear spaces of homogeneous polynomials and to linear spaces of vector-valued Lispshitz functions on metric spaces. |
| title | Spaceability of sets of non-injective maps |
| topic | Functional Analysis 15A03, 46B87, 47B10 |
| url | https://arxiv.org/abs/2403.19855 |