A. Avilés

activity

20082019

most citedBanach spaces of universal disposition

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

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10 papers · 1 filter

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.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.FA2016★ 1 cited

Convex combinations of weak*-convergent sequences and the Mackey topology

Antonio Avilés, José Rodríguez

A Banach space $X$ is said to have property (K) if every $w^{*}$ -convergent sequence in $X^{*}$ admits a convex block subsequence which converges with respect to the Mackey topology. W…

math.FA2014

Tukey classification of some ideals in $ω$ and the lattices of weakly compact sets in Banach spaces

Antonio Avilés, Grzegorz Plebanek, José Rodríguez

We study the lattice structure of the family of weakly compact subsets of the unit ball $B_{X}$ of a separable Banach space $X$ , equipped with the inclusion relation (this structure…

math.FA2011★ 41 cited

Banach spaces of universal disposition

Antonio Aviles, Felix Cabello, Jesus M. F. Castillo +2

In this paper we present a method to obtain Banach spaces of universal and almost-universal disposition with respect to a given class $M$ of normed spaces. The method pro…

On the Banach lattice c_0

The free Banach lattices generated by ℓp​ and c0​

Boolean-valued models as a foundation for locally L0-convex analysis and Conditional set theory

Convex combinations of weak*-convergent sequences and the Mackey topology

Tukey classification of some ideals in ω and the lattices of weakly compact sets in Banach spaces

Banach spaces of universal disposition

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

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

Tukey classification of some ideals in $ω$ and the lattices of weakly compact sets in Banach spaces