A. Avilés

activity

20082019

most citedBanach spaces of universal disposition

41 citations · 58 across the 19 of their papers we have counts for

collaborators

19 papers

math.FA2019★ 7 cited

On the Banach lattice c_0

Antonio Avilés, Gonzalo Martínez-Cervantes, José David Rodríguez Abellán

We show that $c_{0}$ is not a projective Banach lattice, answering a question of B. de Pagter and A. Wickstead. On the other hand, we show that $c_{0}$ is complemented in the free Bana…

math.LO2019

Splitting chains, tunnels and twisted sums

Félix Cabello Sánchez, Antonio Avilés, Piotr Borodulin-Nadzieja +2

We study splitting chains in $P (ω)$ , that is, families of subsets of $ω$ which are linearly ordered by $\subseteq^{*}$ and which are splitting. We prove that their existenc…

math.GN2018

On fragmentable compact lines

Antonio Avilés, Gonzalo Martínez-Cervantes, Grzegorz Plebanek +1

We prove that if a compact line is fragmentable, then it is a Radon-Nikodým compact space.

math.FA2018

The free Banach lattices generated by $ℓ_{p}$ and $c_{0}$

Antonio Avilés, Pedro Tradacete, Ignacio Villanueva

We prove that, when $2 < p < \infty$ , in the free Banach lattice generated by $ℓ_{p}$ (respectively by $c_{0}$ ), the absolute values of the canonical basis form an $ℓ_{r}$ -sequence, wh…

math.FA2017★ 2 cited

Boolean-valued models as a foundation for locally $L^{0}$ -convex analysis and Conditional set theory

Antonio Avilés, José Miguel Zapata

Locally $L^{0}$ -convex modules were introduced in [D. Filipovic, M. Kupper, N. Vogelpoth. Separation and duality in locally $L^{0}$ -convex modules. J. Funct. Anal. 256(12), 3996-4029 (…

math.LO2016

Free sets for a set-mapping relative to a family of sets

Antonio Avilés, Claribet Piña

Given a family $F$ of subsets of ${1, \dots, m}$ , we try to compute the least natural number $n$ such that for every function $S:[\aleph_n]^{<ω}\longrightarrow [\aleph_n…