arXiv subjects

María D. Acosta

Publications and source records attributed to María D. Acosta.

3 recordsLinked to original sources

arXiv2021

Bishop-Phelps-Bollobás property for positive operators when the domain is $C_0(L) $

Recently it was introduced the so-called Bishop-Phelps-Bollob{á}s property for positive operators between Banach lattices. In this paper we prove that the pair $(C_0(L), Y) $ has the Bishop-Phelps--Bollob{á}s property for positive operators, for any locally compact Hausdorff topological space $L$, whenever $Y$ is a uniformly monotone Banach lattice with a weak unit. In case that the space $C_0(L)$ is separable, the same statement holds for any uniformly monotone Banach lattice $Y .$ We also show the following partial converse of the main result. In case that $Y$ is a strictly monotone Banach lattice, $L$ is a locally compact Hausdorff topological space that contains at least two elements and the pair $(C_0(L), Y )$ has the Bishop-Phelps--Bollob{á}s property for positive operators then $Y$ is uniformly monotone.

math.FA↗

arXiv2019

Bishop-Phelps-Bollobás property for positive operators between classical Banach spaces

We prove that the class of positive operators from $L_\infty (μ)$ to $L_1 (ν)$ has the Bishop-Phelps-Bollobás property for any positive measures $μ$ and $ν$. The same result also holds for the pair $(c_0, \ell_1)$. We also provide an example showing that not every pair of Banach lattices satisfies the Bishop-Phelps-Bollobás property for positive operators.

math.FA↗

arXiv2018

Characterization of Banach spaces $Y$ satisfying that the pair $ (\ell_\infty^4,Y )$ has the Bishop-Phelps-Bollobás property for operators

We study the Bishop-Phelps-Bollobás property for operators from $\ell_\infty ^4 $ to a Banach space. For this reason we introduce an appropiate geometric property, namely the AHSp-$\ell_\infty ^4$. We prove that spaces $Y$satisfying AHSp-$\ell_\infty ^4$ are precisely those spaces $Y$ such that $(\ell_\infty^4,Y)$ has the Bishop-Phelps-Bollobás property. We also provide classes of Banach spaces satisfying this condition. For instance, finite-dimensional spaces, uniformly convex spaces, $C_0(L)$ and $L_1 (μ)$ satisfy AHSp-$\ell_\infty ^4 $.

math.FA↗