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Nazaret Trejo-Arroyo

Publications and source records attributed to Nazaret Trejo-Arroyo.

3 recordsLinked to original sources
arXiv2026

Universal $δ$-functors and relative injective objects in the category of $p$-Banach spaces

Inspired by Grothendieck's foundational work, we establish that the sequence of functors $(Ext^n_{pBan}(E,-))_{n \ge 0}$ on the category of $p$-Banach spaces ($0 < p < 1$) forms a universal $δ$-functor. To this end, for any pair of $p$-Banach spaces $E$ and $X$, we construct a $p$-Banach space $\mathcal N_E^X$ that renders each functor $Ext^n_{pBan}(E,-)$ effaceable. Furthermore, we show that this space serves as a relative injective object for $E$ and $X$, enabling the construction of relative injective presentations and proving that the functors $Ext^n_{pBan}(E,-)$ are the right derived functors of $\mathcal{L}(E,-)$. We will also examine the situation in the category of quasi-Banach spaces.

math.FA↗
arXiv2025

Free quasi-Banach lattices

We study different versions of \emph{free objects} in the setting of quasi-Banach spaces and quasi-Banach lattices. Special attention is devoted to the free $p$-convex $p$-Banach lattice $\operatorname{FpBL}^{(p)}[E]$ generated by a $p$-natural quasi-Banach space $E$, for which we provide a functional representation by means of operators into $L_p[0,1]$. This representation yields, among other consequences: (1) Operators from a Banach space $E$ to any $p$-convex $(0<p<1)$ quasi-Banach lattice $X$ can be extended to lattice homomorphisms $\operatorname{FBL}[E] \to X$ with control of the norm. (2) The space $\ell_p(Γ)$ $(0<p<1)$ is a projective $p$-Banach lattice precisely when $Γ$ is countable. (3) The free vector lattice generated by $E$ sits inside $\operatorname{FpBL}^{(p)}[E]$ as a dense sublattice.

math.FA↗