Abraham Rueda Zoca

Transfinite octahedrality in spaces of operators

Abraham Rueda Zoca

We study necessary and sufficient conditions on a Banach space $X$ such that $L (Y, X)$ is transfinite (rigid) octahedral for any Banach space $Y$ . We present several examples of suc…

Projective norm-attainments and their implications

Manwook Han, Sun Kwang Kim, Miguel Martín +1

We show that nuclear norm-attaining operators (resp.\ polynomials) are always $w^{*}$ -dense in the space of integral operators (resp.\ polynomials). Besides, the denseness is in norm…

Differences between the uniform diameter two properties

Abraham Rueda Zoca

We study uniform versions of the diameter two properties, that is, the uniform slice-D2P, the uniform D2P and the uniform SD2P, as the property that every ultrapower over any free…

Strongly regular Banach spaces with big weakly open subsets in the unit ball

Ginés López-Pérez, Abraham Rueda Zoca

We construct, given $1 < p < \infty$ , a Banach space $Y$ and a closed, convex and symmetric set $L \subseteq B_{Y}$ with the following properties: 1) $Y^{**}$ is strongly regular (hencefo…

Banach spaces with the weak diametral diameter two property

Juan Guerrero-Viu, Miguel Martín, Abraham Rueda Zoca

We introduce and systematically study the weak diametral diameter two property (weak-DD2P), a new geometric property that lies strictly between the diametral diameter two property…

Transfinite Daugavet property

Antonio Avilés, Johann Langemets, Miguel Martín +1

We extend the Daugavet property and a perfect version of it to transfinite cardinals in order to distinguish between spaces with the ordinary Daugavet property by some kind of comp…

The uniform strong diameter two property

Esteban Martínez Vañó, Abraham Rueda Zoca

We study a uniform version of the strong diameter two property. In particular, we find a characterisation that does not involve ultrafilters and we use it to provide some examples…

Big weak open radius versus big slice diameter

Ginés López-Pérez, Esteban Martínez Vañó, Abraham Rueda Zoca

We show that there exists a Banach space in which every non-empty weakly open subset of its unit ball has radius one, the maximum possible value, but the infimum of the diameter of…

Almost preserved extreme points

Ramón J. Aliaga, Luis C. García-Lirola, Juan Guerrero-Viu +2

In this paper we introduce the notion of an almost preserved extreme point (APEP) of a set as a weakening of the concept of preserved extreme points, and we systematically study su…

The super Alternative Daugavet property for Banach spaces

Johann Langemets, Marcus Lõo, Miguel Martín +2

We introduce the super alternative Daugavet property (super ADP) which lies strictly between the Daugavet property and the Alternative Daugavet property as follows. A Banach space…

Lipschitz interpolating sequences

A. Jiménez-Vargas, Abraham Rueda Zoca

Let $X$ be a metric space with a base point $0$ , and let $Lip_{0} (X)$ be the Banach space of all Lipschitz functions $f : X ⟶ R$ such that $f (0) = 0$ . Given…

math.FA2024

New examples of strongly subdifferentiable projective tensor products

Abraham Rueda Zoca

We prove that the norm of $X \otimes_{π} Y$ is SSD if either $X = ℓ_{p} (I)$ for $p > 2$ and $Y$ is a finite-dimensional Banach space such that the modulus of convexity is of pow…

Slicely countably determined points in Banach spaces

Johann Langemets, Marcus Lõo, Miguel Martin +1

We introduce slicely countably determined points (SCD points) of a bounded and convex subset of a Banach space which extends the notions of denting points, strongly regular points…

Banach spaces with small weakly open subsets of the unit ball and massive sets of Daugavet and $Δ$ -points

Christian Cobollo, Daniel Isert, Ginés López-Pérez +6

We prove that there exists an equivalent norm $∥∣ \cdot ∣∥$ on $L_{\infty} [0, 1]$ with the following properties: (1) The unit ball of $(L_\infty[0,1],\Vert\vert\cdot\ver…

Diameter, radius and Daugavet index of thickness of slices in Banach spaces

Abraham Rueda Zoca

We construct a Banach space $X$ with the r-BSP such that the infimum of the diameter of the slices of the unit ball is $1$ , which gives negative answer to a 2006 question by Y. Iva…

Weak precompactness in projective tensor products

José Rodríguez, Abraham Rueda Zoca

We give a sufficient condition for a pair of Banach spaces $(X, Y)$ to have the following property: whenever $W_{1} \subseteq X$ and $W_{2} \subseteq Y$ are sets such that $\{x\otimes y…

A characterisation of the Daugavet property in spaces of vector-valued Lipschitz functions

Rubén Medina, Abraham Rueda Zoca

Let $M$ be a metric space and $X$ be a Banach space. In this paper we address several questions about the structure of $F (M) \otimes_{π} X$ and $L i p (M, X)$ .…

math.FA2023★ 1 cited

Diametral notions for elements of the unit ball of a Banach space

Miguel Martin, Yoël Perreau, Abraham Rueda Zoca

We introduce extensions of $Δ$ -points and Daugavet points in which slices are replaced by relative weakly open subsets (super $Δ$ -points and super Daugavet points) or by convex com…

Transfinite almost square Banach spaces

Antonio Avilés, Stefano Ciaci, Johann Langemets +2

It is known that a Banach space contains an isomorphic copy of $c_{0}$ if, and only if, it can be equivalently renormed to be almost square. We introduce and study transfinite versio…

Infinite dimensional spaces in the set of strongly norm-attaining Lipschitz maps

Antonio Avilés, Gonzalo Martínez-Cervantes, Abraham Rueda Zoca +1

We prove that if $M$ is an infinite complete metric space then the set of strongly norm-attaining Lipschitz functions $\SA(M)$ contains a linear subspace isomorphic to $c_{0}$ . This…

math.FA2022★ 11 cited

Residuality in the set of norm attaining operators between Banach spaces

Mingu Jung, Miguel Martin, Abraham Rueda Zoca

We study the relationship between the residuality of the set of norm attaining functionals on a Banach space and the residuality and the denseness of the set of norm attaining oper…

The Daugavet property in spaces of vector-valued Lipschitz functions

Abraham Rueda Zoca

We prove that if a metric space $M$ has the finite CEP then $F (M) \otimes_{π} X$ has the Daugavet property for every non-zero Banach space $X$ . This applies, for in…