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The support localization property of the strongly embedded subspaces of banach function spaces

El archivo no es la versión final publicada del trabajo.[EN] Motivated by the well known Kadec-Pelczynski disjointifcation theorem, we undertake an analysis of the supports of non-zero functions in strongly embedded subspaces of Banach functions spaces. The main aim is to isolate those properties that bring additional information on strongly embedded subspaces. This is the case of the support localization property, which is a necessary condition fulflled by all strongly embedded subspaces. Several examples that involve Rademacher functions, the Volterra operator, Lorentz spaces or Orlicz spaces are provided.P. Rueda acknowledges with thanks the support of the Ministerio de Econom´ıa y Competitividad (Spain) MTM2011-22417. E. A. S´anchez P´erez acknowledges with thanks the support of the Ministerio de Econom´ıa y Competitividad (Spain) MTM2012-36740-C02-02.Rueda, P.; Sánchez Pérez, EA. (2015). The support localization property of the strongly embedded subspaces of banach function spaces. Studia Scientiarum Mathematicarum Hungarica. 52(4):559-576. https://doi.org/10.1556/012.2015.1326S55957652

Closed injective ideals of multilinear operators, related measures and interpolation

This is the peer reviewed version of the following article: Manzano, A, Rueda, P, Sánchez-Pérez, EA. Closed injective ideals of multilinear operators, related measures and interpolation. Mathematische Nachrichten. 2020; 293: 510-532, which has been published in final form at https://doi.org/10.1002/mana.201800415. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.[EN] We introduce and discuss several ways of extending the inner measure arisen from the closed injective hull of an ideal of linear operators to the multilinear case. In particular, we consider new measures that allow to characterize the operators that belong to a closed injective ideal of multilinear operators as those having measure equal to zero. Some interpolation formulas for these measures, and consequently interpolation results involving ideals of multilinear operators, are established. Examples and applications related to summing multilinear operators are also shown.Ministerio de Economia, Industria y Competitividad and FEDER, Grant/Award Numbers: MTM2016-77054-C2-1-P, MTM2017-84058-PManzano, A.; Rueda, P.; Sánchez Pérez, EA. (2020). Closed injective ideals of multilinear operators, related measures and interpolation. Mathematische Nachrichten. 293(3):510-532. https://doi.org/10.1002/mana.201800415S5105322933Arens, R. (1951). The adjoint of a bilinear operation. Proceedings of the American Mathematical Society, 2(6), 839-848. doi:10.1090/s0002-9939-1951-0045941-1Aron, R. M., & Berner, P. D. (1978). A Hahn-Banach extension theorem for analytic mappings. Bulletin de la Société mathématique de France, 79, 3-24. doi:10.24033/bsmf.1862Aron, R. M., Cole, B. J., & Gamelin, T. W. (1995). Weak-Star Continuous Analytic Functions. Canadian Journal of Mathematics, 47(4), 673-683. doi:10.4153/cjm-1995-035-1Bergh, J., & Löfström, J. (1976). Interpolation Spaces. Grundlehren der mathematischen Wissenschaften. doi:10.1007/978-3-642-66451-9Besoy, B. F., & Cobos, F. (2019). Interpolation of the measure of non-compactness of bilinear operators among quasi-Banach spaces. Journal of Approximation Theory, 243, 25-44. doi:10.1016/j.jat.2019.03.004Beucher, O. J. (1989). On interpolation of strictly (co-)singular linear operators. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 112(3-4), 263-269. doi:10.1017/s0308210500018734Botelho, G. (2002). Weakly Compact and Absolutely Summing Polynomials. Journal of Mathematical Analysis and Applications, 265(2), 458-462. doi:10.1006/jmaa.2001.7674Botelho, G., Pellegrino, D., & Rueda, P. (2007). On Composition Ideals of Multilinear Mappings and Homogeneous Polynomials. Publications of the Research Institute for Mathematical Sciences, 43(4), 1139-1155. doi:10.2977/prims/1201012383Braunss, H.-A., & Junek, H. (2004). Factorization of injective ideals by interpolation. Journal of Mathematical Analysis and Applications, 297(2), 740-750. doi:10.1016/j.jmaa.2004.04.045Cobos, F. (1999). Interpolation theory and measures related to operator ideals. The Quarterly Journal of Mathematics, 50(200), 401-416. doi:10.1093/qjmath/50.200.401Cobos, F., Manzano, A., Martínez, A., & Matos, P. (2000). On interpolation of strictly singular operators, strictly co-singular operators and related operator ideals. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 130(5), 971-989. doi:10.1017/s0308210500000524Cobos, F., & Martínez, A. (1999). Remarks on Interpolation Properties of the Measure of Weak Non -- Compactness and Ideal Variations. Mathematische Nachrichten, 208(1), 93-100. doi:10.1002/mana.3212080104Dahia, E., Achour, D., & Sánchez Pérez, E. A. (2013). Absolutely continuous multilinear operators. Journal of Mathematical Analysis and Applications, 397(1), 205-224. doi:10.1016/j.jmaa.2012.07.034González, M., & Gutiérrez, J. M. (1999). Injective factorization of holomorphic mappings. Proceedings of the American Mathematical Society, 127(6), 1715-1721. doi:10.1090/s0002-9939-99-04917-5González, M., & Gutiérrez, J. (2000). Erratum to «Injective factorization of holomorphic mappings». Proceedings of the American Mathematical Society, 129(4), 1255-1256. doi:10.1090/s0002-9939-00-06055-xGrothendieck, A. (1954). Sur Certains Sous-Espaces Vectoriels De Lp. Canadian Journal of Mathematics, 6, 158-160. doi:10.4153/cjm-1954-017-xHeinrich, S. (1980). Closed operator ideals and interpolation. Journal of Functional Analysis, 35(3), 397-411. doi:10.1016/0022-1236(80)90089-0Jarchow, H. (1981). Locally Convex Spaces. Mathematische Leitfäden. doi:10.1007/978-3-322-90559-8Kato, T. (1958). Perturbation theory for nullity, deficiency and other quantities of linear operators. Journal d’Analyse Mathématique, 6(1), 261-322. doi:10.1007/bf02790238López Molina, J. A., & Sánchez Pérez, E. A. (2000). On operator ideals related to (p,σ)-absolutely continuous operators. Studia Mathematica, 138(1), 25-40. doi:10.4064/sm-138-1-25-40Maligranda, L. (1986). Interpolation between sum and intersection of Banach spaces. Journal of Approximation Theory, 47(1), 42-53. doi:10.1016/0021-9045(86)90045-6Maligranda, L., & Quevedo, A. (1990). Interpolation of weakly compact operators. Archiv der Mathematik, 55(3), 280-284. doi:10.1007/bf01191169Matter, U. (1987). Absolutely Continuous Operators and Super-Reflexivity. Mathematische Nachrichten, 130(1), 193-216. doi:10.1002/mana.19871300118Pellegrino, D., Rueda, P., & Sánchez-Pérez, E. A. (2015). 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. doi:10.1007/s13398-015-0224-8A.Pietsch Ideals of multilinear functionals (designs of a theory) Proceedings of the Second International Conference on Operator Algebras Ideals and Their Applications in Theoretical Physics Teubner‐Texte Math. vol. 67 Teubner Leipzig 1983 pp.185–199.Popa, D. (2016). A note on the concept of factorable strongly p-summing operators. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 111(2), 465-471. doi:10.1007/s13398-016-0307-1Tylli, H.-O. (1995). The essential norm of an operator is not self-dual. Israel Journal of Mathematics, 91(1-3), 93-110. doi:10.1007/bf0276164

Closed surjective ideals of multilinear operators and interpolation

[EN] In this paper we introduce a function for multilinear operators that can be considered as an extension of the so-called outer measure associated to a linear operator ideal. We prove that it allows to characterize the operators that belong to a closed surjective ideal of multilinear operators as those having measure equal to zero. We also obtain some interpolation formulas for this new measure. As a consequence we deduce interpolation results for arbitrary closed surjective ideals of multilinear operators which recover, in particular, different results previously established in the literature.The authors would like to thank the referees for their useful comments which have led to improve the paper. A. Manzano was supported in part by the Ministerio de Economia, Industria y Competitividad and FEDER under project MTM2017-84058-P. P. Rueda and E. A. Sanchez-Perez were supported in part by the Ministerio de Economia, Industria y Competitividad and FEDER under project MTM2016-77054-C2-1-P.Manzano, A.; Rueda, P.; Sánchez Pérez, EA. (2021). Closed surjective ideals of multilinear operators and interpolation. Banach Journal of Mathematical Analysis. 15(2):1-22. https://doi.org/10.1007/s43037-020-00115-512215

Compactness in spaces of p-integrable functions with respect to a vector measure

The final publication is available at the TMNA webpage via http://dx.doi.org/10.12775/TMNA.2015.030.[EN] We prove that, under some reasonable requirements, the unit balls of the spaces Lp(m) and Loo(m) of a vector measure of compact range m are compact with respect to the topology t_m of pointwise convergence of the integrals. This result can be considered as a generalization of the classical Alaoglu Theorem to spaces of p-integrable functions with respect to vector measures with relatively compact range. Some applications to the analysis of the Saks spaces defined by the norm topology and t_m are given.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.Rueda Segado, MP.; Sánchez Pérez, EA. (2015). Compactness in spaces of p-integrable functions with respect to a vector measure. Topological Methods in Nonlinear Analysis. 45(2):641-653. https://doi.org/10.12775/TMNA.2015.03064165345

EXTENSION OF LIPSCHITZ-TYPE OPERATORS ON BANACH FUNCTION SPACES

[EN] We study extension theorems for Lipschitz-type operators acting on metric spaces and with values on spaces of integrable functions. Pointwise domination is not a natural feature of such spaces, and so almost everywhere inequalities and other measure-theoretic notions are introduced. We analyze Lipschitz-type inequalities in two fundamental cases. The first concerns almost everywhere pointwise inequalities, while the second considers dominations involving integrals. These Lipschitz-type inequalities provide a suitable frame to work with operators that take values on Banach function spaces. In the last part of the paper we use some interpolation procedures to extend our study to interpolated Banach function spaces.The second and the third authors gratefully acknowledge the support of the Ministerio de Ciencia, Innovacion y Universidades (Spain) and FEDER under grant MTM2016-77054-C2-1-P2Cavalcante, WV.; Rueda, P.; Sánchez Pérez, EA. (2021). EXTENSION OF LIPSCHITZ-TYPE OPERATORS ON BANACH FUNCTION SPACES. Topological Methods in Nonlinear Analysis. 57(1):343-364. https://doi.org/10.12775/TMNA.2020.026S34336457

Fibrosis glútea: ¿esencial o secundaria?

Constatamos la rara frecuencia de esta afección presentando 5 observaciones de Fibrosis Glútea recogidas en tres casos clínicos estudiados. Dos son bilaterales y uno afecta a un solo glúteo. Habiéndose invocado, por los autores consultados, etiologías diversas, actualmente sigue siendo desconocida. Creemos de interés resaltar que los casos presentados se trataron en las etapas finales de crecimiento, mientras que los referidos en la literatura consultada todos han recibido tratamiento quirúrgico en edad temprana. El tratamiento es de resultado satisfactorio, independientemente de la edad y de la técnica quirúrgica empleada.Three patients affected with gluteal fibrosis are colected by the authors. Two cases had bilateral presentation and one patient was unilateral. According to the literature, the aetiology continue to be unknow. All patients were treated at the end of growthing period, while all cases collected in the literature were treated early. The results have been satisfactory without relation to age or the surgical procedure employed

Propuesta de intervención con alumnos con altas capacidades en el aula de Primaria de un Centro Rural Agrupado de Aragón

Actualmente, el abordaje de la sobredotación no es una realidad manifiesta en colegios alejados de los núcleos con alta población en la Comunidad de Aragón. El presente trabajo pretende ser un elemento facilitador del desarrollo de las altas capacidades en alumnos de Centros Rurales Agrupados. Esto hace que nos planteemos la necesidad de atender las necesidades educativas especiales de estos alumnos lo mejor posible. El trabajo consta de dos grandes bloques. El primero desarrolla un marco teórico en el que se realiza una delimitación y conceptualización del constructo de inteligencia, de las diferentes teorías relativas a ésta y, paralelamente, sobre la sobredotación. Se aborda la respuesta educativa ante las altas capacidades y los recursos que nos aportan las diferentes administraciones para el tratamiento de las mismas. Entre los puntos más notables se encuentra el programa de profundización de conocimientos. Así pues, el segundo se centra en una propuesta de intervención que desarrollar y particulariza en el contexto de los centros rurales dicho programa de profundización. Para ello, se trabajan varias competencias (lingüística, matemática, creativa y tecnológica) a través de talleres específicos con alumnos con sobredotación. Se espera que una vez implementado el mismo este tipo de alumnos pueda desarrollar y mejorar su potencial

c-Src signaling in triple negative breast cancer cells: role of Cyr61

Póster presentado al CNIO Frontiers Meeting: "Metastasis Initiation: Mechanistic Insights and Therapeutic Opportunities", celebrado en el Spanish National Cancer Research Centre (CNIO) Auditorium del 28 al 30 de septiembre de 2015.The SFKs (Src Family Kinases) control cellular pathways involved in division, motility, adhesion, angiogenesis, and survival. Therefore, their deregulation is associated with tumorigenesis, and metastasis. c-Src is overexpressed and/or aberrantly activated in epithelial tumors: pancreatic, colorectal, prostatic, ovarian, breast, etc. We previously showed that SFKs catalytic inhibitors (Dasatinib, PP2, and SU6656) reduce proliferation, migration, and invasiveness of MDA-MB-231. Here, we analyzed c-Src contribution to initial steps of metastasis by Tet-On conditional expression of a specific shRNA-c-Src, which suppressed c-Src mRNA and protein levels in MDA-MB-231. c-Src suppression did not alter cell proliferation or survival, but it significantly reduced anchorage-independent growth. Concomitantly with diminished tyrosine-phosphorylation/activation of Fak, caveolin-1, paxillin and p130CAS, c-Src depletion inhibited migration, invasion, transendothelial migration, and reduced MMP2, MMP7 and MMP9 in secretome. Quantitative proteomic analyses of secretome showed that Cyr61 levels, detected in exosomal fraction, were diminished upon shRNA-c-Src expression. However, Cyr61 expression was unaltered inside cells. Cyr61 partially colocalized with cis-Golgi gp74 marker, and with exosomal marker CD63, but c-Src depletion did not alter their distribution. In SUM159PT, transient c-Src suppression also reduced secreted exosomal Cyr61. Furthermore, conditional expression of c-Src dominant negative mutant (c-Src-K295M/Y527F) in MDA-MB-231 and in SUM159PT diminished secreted Cyr61 as well. Cyr61 transient suppression in MDA-MB-231 inhibited invasion and transendothelial migration. Finally, in both MDA-MB-231 and SUM159PT, a neutralizing Cyr61 antibody restrained migration. Collectively, these results suggest that c-Src regulates secreted proteins, including exosomal Cyr61, which are involved in modulating the metastatic potential of triple negative breast cancer cells.Peer Reviewe