Dunford-Pettis-like Properties of Continuous Vector Function Spaces

Sin resume

Banach spaces in various positions

AbstractWe formulate a general theory of positions for subspaces of a Banach space: we define equivalent and isomorphic positions, study the automorphy index a(Y,X) that measures how many non-equivalent positions Y admits in X, and obtain estimates of a(Y,X) for X a classical Banach space such as ℓp,Lp,L1,C(ωω) or C[0,1]. Then, we study different aspects of the automorphic space problem posed by Lindenstrauss and Rosenthal; namely, does there exist a separable automorphic space different from c0 or ℓ2? Recall that a Banach space X is said to be automorphic if every subspace Y admits only one position in X; i.e., a(Y,X)=1 for every subspace Y of X. We study the notion of extensible space and uniformly finitely extensible space (UFO), which are relevant since every automorphic space is extensible and every extensible space is UFO. We obtain a dichotomy theorem: Every UFO must be either an L∞-space or a weak type 2 near-Hilbert space with the Maurey projection property. We show that a Banach space all of whose subspaces are UFO (called hereditarily UFO spaces) must be asymptotically Hilbertian; while a Banach space for which both X and X∗ are UFO must be weak Hilbert. We then refine the dichotomy theorem for Banach spaces with some additional structure. In particular, we show that an UFO with unconditional basis must be either c0 or a superreflexive weak type 2 space; that a hereditarily UFO Köthe function space must be Hilbert; and that a rearrangement invariant space UFO must be either L∞ or a superreflexive type 2 Banach lattice

Extension of bilinear forms from subespaces of L1 -space

We study the extension of bilinear forms from a given subspace of an L1 -space to the whole space. Precisely, an isomorphic embedding j: E → X is said to be (linearly) 2-exact if bilinear forms on E can be (linear and continuously) extended to X through j . We present some necesary and some sufficient conditions for an embedding j: E → X to be 2-exact when X is an L1 -space

Dunford-Pettis-like Properties of Projective and Natural Tensor Product Spaces

Sin resume

Three-operator problems in Banach spaces

ABSTRACT: We study the analogue of 3-space problems for classes of operators acting on Banach spaces. We show examples of classes of operators having or failing the 3-operator property, and give several methods to obtain classes with this property.The research of the first author was supported in part by Project IB16056 de la Junta de Extremadura; that of the first and third authors was supported in part by MINECO (Spain), Project MTM2016-76958. This paper benefited from a stay in 2016 of Castillo and González at Kanagawa University invited by Prof. Cho

Classes of operators preserved by extensions or liftings

A standard way to obtain extensions (resp. liftings) of operators is by making the so-called operations of push-out (resp. pull-back). In this paper we study the preservation of some classes of operators associated with an operator ideal Aunder push-out extensions or pull-back liftings. We show several examples of classical operator ideals whose associated classes are preserved, we prove that the preservation of those classes under push-out extension or pull-back lifting implies that the space ideal of Asatisfies the 3-space property, and we derive some results for Athat are useful in the study of commutative diagrams of operators.that of the three authors has been supported in part by MINECO (Spain), Project MTM2016-76958

Banach spaces of universal disposition

In this paper we present a method to obtain Banach spaces of universal and almost-universal disposition with respect to a given class $\mathfrak M$ of normed spaces. The method produces, among other, the Gurari\u{\i} space $\mathcal G$ (the only separable Banach space of almost-universal disposition with respect to the class $\mathfrak F$ of finite dimensional spaces), or the Kubis space $\mathcal K$ (under {\sf CH}, the only Banach space with the density character the continuum which is of universal disposition with respect to the class $\mathfrak S$ of separable spaces). We moreover show that $\mathcal K$ is not isomorphic to a subspace of any $C(K)$-space -- which provides a partial answer to the injective space problem-- and that --under {\sf CH}-- it is isomorphic to an ultrapower of the Gurari\u{\i} space. We study further properties of spaces of universal disposition: separable injectivity, partially automorphic character and uniqueness properties

Impacto en el Rendimiento Académico por la Pandemia Covid-19, en los Alumnos de Contador Público del Instituto Tecnológico de Cd. Guzmán

The purpose of this research is to disseminate the impact on academic performance by the COVID-19 pandemic of public accountant students from the Technological Institute of Cd. Guzmán ITCG, as a consequence of virtual classes. This study presents the results of a survey carried out in which they answered openly if online classes affected their academic performance and what factors influenced during the pandemic. Although it was believed that students live immersed in the world of technology, this drastic change made us rethink whether teachers and students are prepared to face the challenges of virtual education, especially when it was the result of a forced adaptation. . This will serve as a reference for teachers and educational institutions to have a clear vision of the current situation of students in the return to face-to-face classes, having the background of the academic performance obtained from online learning. In addition, the emotional situation in which they were involved in where they had the need to face different family situations, health among others.La presente investigación tiene como finalidad divulgar el impacto en el rendimiento académico por la pandemia COVID-19 de los alumnos de contador público del Instituto Tecnológico de Cd. Guzmán ITCG, como consecuencia de las clases virtuales. En este estudio se presentan los resultados de una encuesta realizada la cual contestaron abiertamente si las clases en línea afectaron su rendimiento académico y qué factores influyeron durante la pandemia. Si bien se creía que los estudiantes viven inmersos en el mundo de la tecnología, este cambio tan drástico hizo replantear si los maestros y alumnos, están preparados para afrontar los desafíos de una educación virtual, en especial, cuando ésta fue fruto de una adaptación forzosa. Esto servirá de referencia para que los docentes e instituciones educativas, tengan una visión clara de la situación actual de los educandos en el regreso a clases presenciales, teniendo el antecedente del rendimiento académico obtenido del aprendizaje en línea. Además, de la situación emocional en la que estuvieron involucrados en donde tuvieron la necesidad de enfrentar diferentes situaciones familiares, de salud entre otras

Highly-parallelized simulation of a pixelated LArTPC on a GPU

The rapid development of general-purpose computing on graphics processing units (GPGPU) is allowing the implementation of highly-parallelized Monte Carlo simulation chains for particle physics experiments. This technique is particularly suitable for the simulation of a pixelated charge readout for time projection chambers, given the large number of channels that this technology employs. Here we present the first implementation of a full microphysical simulator of a liquid argon time projection chamber (LArTPC) equipped with light readout and pixelated charge readout, developed for the DUNE Near Detector. The software is implemented with an end-to-end set of GPU-optimized algorithms. The algorithms have been written in Python and translated into CUDA kernels using Numba, a just-in-time compiler for a subset of Python and NumPy instructions. The GPU implementation achieves a speed up of four orders of magnitude compared with the equivalent CPU version. The simulation of the current induced on 10^3 pixels takes around 1 ms on the GPU, compared with approximately 10 s on the CPU. The results of the simulation are compared against data from a pixel-readout LArTPC prototype