On the Dunford-Pettis Property of the Tensor product of C(K) spaces

We characterize those compact Hausdorff spaces K such that the proyective tensor product of C(K) by itself has the Dunford-Pettis Property, answering thus in the negative a question posed by Castillo and Gonzalez.Comment: 5 page

SMS MAMÁ: TeleSalud aplicada a la gestión de pacientes vía SMS

La investigación-acción consiste sondear el universo de población en Mendoza, en condición de embarazo y realizaracciones preventivas destinadas a la población materna-infantil mediante el uso de las Tecnologías de la Información y lasComunicaciones (TIC) a través de un proyecto socio-sanitario destinado a embarazos de alto riesgo, una importanteproblemática de salud pública por sus elevados niveles de morbimortalidad.La herramienta teleinformática utilizada es un sistema web implementado en un Smartphone con sistema operativo Android,donde corren los servicios de datos, de envío y recepción de mensajes de texto (SMS) y el servidor web que responde a las consultas de los clientes enviándolas a la aplicación. Teniendo en cuenta que el número de dispositivos móviles supera la cantidad de habitantes de la República Argentina, se ve la existencia de una gran probabilidad de que las mujeres embarazadas dispongan y sepan utilizar un teléfono móvil para recibir mensajes de texto y de esta forma, realizar las acciones preventivas propuestas. Una cualidad particular de este trabajo es que la aplicación web está compactada en el celular, sin necesidad de instalar e implementar todos estos servicios en una computadora; por lo tanto solo con este dispositivo es posible gestionar campañas, pacientes, estadísticas, y el envío de los SMS

Unbounded violation of tripartite Bell inequalities

We prove that there are tripartite quantum states (constructed from random unitaries) that can lead to arbitrarily large violations of Bell inequalities for dichotomic observables. As a consequence these states can withstand an arbitrary amount of white noise before they admit a description within a local hidden variable model. This is in sharp contrast with the bipartite case, where all violations are bounded by Grothendieck's constant. We will discuss the possibility of determining the Hilbert space dimension from the obtained violation and comment on implications for communication complexity theory. Moreover, we show that the violation obtained from generalized GHZ states is always bounded so that, in contrast to many other contexts, GHZ states do in this case not lead to extremal quantum correlations. The results are based on tools from the theories of operator spaces and tensor norms which we exploit to prove the existence of bounded but not completely bounded trilinear forms from commutative C*-algebras.Comment: Substantial changes in the presentation to make the paper more accessible for a non-specialized reade

Surveying the spirit of absolute summability on multilinear operators and homogeneous polynomials

[EN] We draw a fundamental compendium of the most valuable results of the theory of summing linear operators and detail those that are not shared by known multilinear and polynomial extensions of absolutely summing linear operators. The lack of such results in the theory of non-linear summing operators justifies the introduction of a class of polynomials and multilinear operators that satisfies at once all related non-linear results. Surprisingly enough, this class, defined by means of a summing inequality, happens to be the well known ideal of composition with a summing operator.D. Pellegrino acknowledges with thanks the support of CNPq Grant 401735/2013-3-PVE (Linha 2)-Brazil. P. Rueda acknowledges with thanks the support of the Ministerio de Economia y Competitividad (Spain) MTM2011-22417. E. A. Sanchez Perez acknowledges with thanks the support of the Ministerio de Economia y Competitividad (Spain) MTM2012-36740-C02-02.Pellegrino, D.; Rueda, P.; Sánchez Pérez, EA. (2016). 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Multilinear operators on C(K,X)C(K,X) spaces

summary:Given Banach spaces~ $X$, $Y$ and a compact Hausdorff space~ $K$, we use polymeasures to give necessary conditions for a multilinear operator from $C(K,X)$ into~ $Y$ to be completely continuous (resp.~ unconditionally converging). We deduce necessary and sufficient conditions for~ $X$ to have the Schur property (resp.~ to contain no copy of~ $c_0$), and for~ $K$ to be scattered. This extends results concerning linear operators

On the multilinear Hausdorff problem of moments

Given a multi-index sequence necessary and sufficient conditions are given for the existence of a regular Borel polymeasure on the unit interval such that . This problem will be called the weak multilinear Hausdorff problemof moments for . Comparison with classical results will allow us to relate the weak multilinear Hausdorff problem with the multivariate Hausdorff problem. A solution to the strong multilinear Hausdorff problem of moments will be provided by exhibiting necessary and sufficient conditions for the existence of a Radon measure on such that where is the -linear moment functional on the space of continuous functions on the unit interval defined by the sequence . Finally the previous results will be used to provide a characterization of a class of weakly harmonizable stochastic processes with bimeasures supported on compact sets