2 citations · 4 across the 12 of their papers we have counts for
19 papers
A negative solution to the complemented subspace problem in Banach lattices
D. de Hevia, G. Martínez-Cervantes, A. Salguero-Alarcón +1
Building on a recent construction of G. Plebanek and the third named author, it is shown that a complemented subspace of a Banach lattice need not be linearly isomorphic to a Banac…
Linear versus lattice embeddings between Banach lattices
Antonio Avilés, Gonzalo Martínez-Cervantes, Abraham Rueda Zoca +1
A well-known classical result states that is linearly embeddable in a Banach lattice if and only if it is lattice embeddable. Improving results of H.P.~Lotz, H.P.~Rosenthal a…
Lattice embeddings in free Banach lattices over lattices
Antonio Avilés, Gonzalo Martínez-Cervantes, José David Rodríguez Abellán +1
In this article we deal with the free Banach lattice generated by a lattice and its behavior with respect to subspaces. In general, any lattice embedding $i\colon \mathbb{L} \longr…
Local complementation in Banach spaces and its preservation under free constructions
Antonio Avilés, Gonzalo Martínez-Cervantes, Abraham Rueda Zoca
In this work we consider natural generalizations of local complementation in Banach spaces, which include Lipschitz-local complementation. We show that all these notions are indeed…
A renorming characterization of Banach spaces containing
Antonio Avilés, Gonzalo Martínez-Cervantes, Abraham Rueda Zoca
A result of G. Godefroy asserts that a Banach space contains an isomorphic copy of if and only if there is an equivalent norm such that, for every finite…
Some remarks on the weak maximizing property
Sheldon Dantas, Mingu Jung, Gonzalo Martínez-Cervantes
A pair of Banach spaces is said to have the weak maximizing property (WMP, for short) if for every bounded linear operator from into , the existence of a non-we…
Abundance of independent sequences in compact spaces and Boolean algebras
Antonio Avilés, Gonzalo Martínez-Cervantes, Grzegorz Plebanek
It follows from a theorem of Rosenthal that a compact space is if and only if every Eberlein continuous image is metrizable. Motivated by this result, for a class of compact…
-orthogonal elements and -orthogonal sequences
Antonio Avilés, Gonzalo Martínez-Cervantes, Abraham Rueda Zoca
Given a Banach space , we say that a sequence in the unit ball of is -orthogonal if for every . On the othe…
Free Banach lattices generated by a lattice and projectivity
Antonio Avilés, Gonzalo Martínez-Cervantes, José David Rodríguez Abellán +1
In this article we deal with the free Banach lattice generated by a lattice . We prove that if is projec…
On weak-extensible subspaces of Banach spaces
G. Martínez-Cervantes, J. Rodríguez
Let be a Banach space and be a closed subspace. We prove that if the quotient is weakly Lindelöf determined or weak Asplund, then for every -converge…
A Godefroy-Kalton principle for free Banach lattices
Antonio Avilés, Gonzalo Martínez-Cervantes, José Rodríguez +1
Motivated by the Lipschitz-lifting property of Banach spaces introduced by Godefroy and Kalton, we consider the lattice-lifting property, which is an analogous notion within the ca…
Norm-attaining lattice homomorphisms
Sheldon Dantas, Gonzalo Martínez-Cervantes, José David Rodríguez Abellán +1
In this paper we study the structure of the set $\mbox{Hom}(X,\mathbb{R})$ of all lattice homomorphisms from a Banach lattice into . Using the relation among lattic…
Complete metric spaces with property (Z) are length metric spaces
Antonio Avilés, Gonzalo Martínez-Cervantes
We prove that every complete metric space with property (Z) is a length space. These answers questions posed by García-Lirola, Procházka and Rueda Zoca, and by Becerra Guerrero, Ló…
Weak-sequential properties of Johnson-Lindenstrauss spaces
Antonio Avilés, Gonzalo Martínez-Cervantes, José Rodríguez
A Banach space is said to have Efremov's property () if every element of the weak-closure of a convex bounded set is the weak-limit of a…
Mardešić conjecture and free products of Boolean algebras
Gonzalo Martínez-Cervantes, Grzegorz Plebanek
We show that for every , if are linearly ordered compact spaces and there is a continuous surjection \[ L_1\times L_2\times \dots\times L_d\to K_1\times K…
Banach spaces with weak*-sequential dual ball
Gonzalo Martínez-Cervantes
A topological space is said to be sequential if every sequentially closed subspace is closed. We consider Banach spaces with weak*-sequential dual ball. In particular, we show that…
Weakly Radon-Nikodým Boolean algebras and independent sequences
Antonio Avilés, Gonzalo Martínez-Cervantes, Grzegorz Plebanek
A compact space is said to be weakly Radon-Nikodým (WRN) if it can be weak*-embedded into the dual of a Banach space not containing . We investigate WRN Boolean algebras, i…
Riemann integrability versus weak continuity
Gonzalo Martínez-Cervantes
In this paper we focus on the relation between Riemann integrability and weak continuity. A Banach space is said to have the weak Lebesgue property if every Riemann integrable…
On weakly Radon-Nikodým compact spaces
Gonzalo Martínez-Cervantes
A compact space is said to be weakly Radon-Nikodým if it is homeomorphic to a weak*-compact subset of the dual of a Banach space not containing an isomorphic copy of . In t…