Spaceability of sets of non-injective maps

2024/03/28 by Aires, Mikaela, Botelho, Geraldo · 1 citation
#15A03 #46B87 #47B10 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2403.19855

Abstract

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 ≠ f ∈ 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.

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