41 research outputs found
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). Surveying the spirit of absolute summability on multilinear operators and homogeneous polynomials. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 110(1):285-302. https://doi.org/10.1007/s13398-015-0224-8S2853021101Achour, D., Dahia, E., Rueda, P., Sánchez-Pérez, E.A.: Factorization of absolutely continuous polynomials. J. Math. Anal. Appl. 405(1), 259–270 (2013)Albiac, F., Kalton, N.: Topics in Banac Space Theory. Springer, Berlin (2005)Alencar, R., Matos, M.C.: Some classes of multilinear mappings between Banach spaces, Publicaciones del Departamento de Análisis Matemático 12, Universidad Complutense Madrid (1989)Bombal, F., Pérez-García, D., Villanueva, I.: Multilinear extensions of Grothendieck’s theorem. Q. J. Math. 55(4), 441–450 (2004)Botelho, G., Braunss, H.-A., Junek, H., Pellegrino, D.: Holomorphy types and ideals of multilinear mappings. Studia Math. 177, 43–65 (2006)Botelho, G., Pellegrino, D.: Scalar-valued dominated polynomials on Banach spaces. Proc. Am. Math. Soc. 134, 1743–1751 (2006)Botelho, G., Pellegrino, D.: Absolutely summing polynomials on Banach spaces with unconditional basis. J. Math. Anal. Appl. 321, 50–58 (2006)Botelho, G., Pellegrino, D.: Coincidence situations for absolutely summing non-linear mappings. Port. Math. (N.S.) 64(2), 175–191 (2007)Botelho, G., Pellegrino, D., Rueda, P.: Pietsch’s factorization theorem for dominated polynomials. J. Funct. Anal. 243(1), 257–269 (2007)Botelho, G., Pellegrino, D., Rueda, P.: On composition ideals of multilinear mappings and homogeneous polynomials. Publ. Res. Inst. Math. Sci. 43(4), 1139–1155 (2007)Botelho, G., Pellegrino, D., Rueda, P.: A unified Pietsch domination theorem. J. Math. Anal. Appl. 365, 269–276 (2010)Botelho, G., Pellegrino, D., Rueda, P.: Dominated polynomials on infinite dimensional spaces. Proc. Am. Math. Soc. 138(1), 209–216 (2010)Botelho, G., Pellegrino, D., Rueda, P.: Cotype and absolutely summing linear operators. Math. Z. 267(1–2), 1–7 (2011)Botelho, G., Pellegrino, D., Rueda, P.: On Pietsch measures for summing operators and dominated polynomials. Linear Multilinear Algebra 62(7), 860–874 (2014)Çalışkan, E., Pellegrino, D.M.: On the multilinear generalizations of the concept of absolutely summing operators. Rocky Mountain J. Math. 37, 1137–1154 (2007)Carando, D., Dimant, V.: On summability of bilinear operators. Math. Nachr. 259, 3–11 (2003)Carando, D., Dimant, V., Muro, S.: Coherent sequences of polynomial ideals on Banach spaces. Math. Nachr. 282, 1111–1133 (2009)Defant, A., Floret, K.: Tensor norms and operator ideals. North-Holland Mathematics Studies, 176. North-Holland Publishing Co., Amsterdam (1993)Diestel, J., Jarchow, H., Tonge, A.: Absolutely summing operators. Cambridge University Press, Cambridge (1995)Dimant, V.: Strongly p -summing multilinear operators. J. Math. Anal. Appl. 278, 182–193 (2003)Dineen, S.: Complex analysis on infinite-dimensional spaces. Springer, London (1999)Fabian, M., Hájek, P., Montesinos-Santalucía, V., Pelant, J., Zizler, V.: Functional analysis and infinite-dimensional geometry. CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, 8. Springer, New York (2001)Floret, K.: Natural norms on symmetric tensor products of normed spaces. Note Mat. 17, 153–188 (1997)Geiss, H.: Ideale multilinearer Abbildungen. Diplomarbeit, Brandenburgische Landeshochschule (1985)Grothendieck, A.: Résumé de la théorie métrique des produits tensoriels topologiques (French). Bol. Soc. Mat. São Paulo 8, 1–79 (1953)Jarchow, H., Palazuelos, C., Pérez-García, D., Villanueva, I.: Hahn-Banach extension of multilinear forms and summability. J. Math. Anal. Appl. 336, 1161–1177 (2007)Lindenstrauss, J., Pełczyński, A.: Absolutely summing operators in L p spaces and their applications. Studia Math. 29, 275–326 (1968)Matos, M.C.: Absolutely summing holomorphic mappings. Anais da Academia Brasileira de Ciências 68, 1–13 (1996)Matos, M.C.: Fully absolutely summing and Hilbert–Schmidt multilinear mappings. Collectanea Math. 54, 111–136 (2003)Matos, M.C.: Nonlinear absolutely summing mappings. Math. Nachr. 258, 71–89 (2003)Meléndez, Y., Tonge, A.: Polynomials and the Pietsch domination theorem. Proc. R. Irish Acad. Sect. A 99, 195–212 (1999)Montanaro, A.: Some applications of hypercontractive inequalities in quantum information theory. J. Math. Phys. 53(12), 122–206 (2012)Mujica, J.: Complex analysis in Banach spaces. Dover Publications, Mineola (2010)Pellegrino, D.: Cotype and absolutely summing homogeneous polynomials in L p spaces. Studia Math. 157, 121–131 (2003)Pellegrino, D., Ribeiro, J.: On multi-ideals and polynomial ideals of Banach spaces: a new approach to coherence and compatibility. Monatsh. Math. 173(3), 379–415 (2014)Pellegrino, D., Santos, J.: A general Pietsch domination theorem. J. Math. Anal. Appl. 375, 371–374 (2011)Pellegrino, D., Santos, J.: Absolutely summing multilinear operators: a panorama. Quaest. Math. 34(4), 447–478 (2011)Pellegrino, D., Santos, J.: On summability of nonlinear mappings: a new approach. Math. Z. 270(1–2), 189–196 (2012)Pellegrino, D., Santos, J., Seoane-Sepúlveda, J.B.: Some techniques on nonlinear analysis and applications. Adv. Math. 229, 1235–1265 (2012)Pérez-García, D.: David Comparing different classes of absolutely summing multilinear operators. Arch. Math. (Basel) 85(3), 258–267 (2005)Pietsch, A.: Absolut p-summierende Abbildungen in normierten Räumen. (German) Studia Math. 28, 333–353 (1966/1967)Pietsch, A.: Ideals of multilinear functionals (designs of a theory). Proceedings of the second international conference on operator algebras, ideals, and their applications in theoretical physics (Leipzig, 1983), 185–199, Teubner-Texte Math., 67, Teubner, Leipzig, (1984)Pisier, G.: Grothendieck’s theorem, past and present. Bull. Am. Math. Soc. (N.S.) 49(2), 237–323 (2012)Rueda, P., Sánchez-Pérez, E.A.: Factorization of p -dominated polynomials through L p -spaces. Michigan Math. J. 63(2), 345–353 (2014)Rueda, P., Sánchez-Pérez, E.A.: Factorization theorems for homogeneous maps on Banach function spaces and approximation of compact operators. Mediterr. J. Math. 12(1), 89–115 (2015)Ryan, R.A.: Applications of Topological Tensor Products to Infinite Dimensional Holomorphy, Ph.D. Thesis, Trinity College, Dublin, (1980
Multilinear operators on spaces
summary:Given Banach spaces~ , and a compact Hausdorff space~ , we use polymeasures to give necessary conditions for a multilinear operator from into~ to be completely continuous (resp.~ unconditionally converging). We deduce necessary and sufficient conditions for~ to have the Schur property (resp.~ to contain no copy of~ ), and for~ 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