On the smoothness of L p of a positive vector measure

The final publication is available at Springer via http://dx.doi.org/10.1007/s00605-014-0666-7We investigate natural sufficient conditions for a space L p(m) of pintegrable functions with respect to a positive vector measure to be smooth. Under some assumptions on the representation of the dual space of such a space, we prove that this is the case for instance if the Banach space where the vector measure takes its values is smooth. We give also some examples and show some applications of our results for determining norm attaining elements for operators between two spaces L p(m1) and Lq (m2) of positive vector measures m1 and m2.Professor Agud and professor Sanchez-Perez authors gratefully acknowledge the support of the Ministerio de Economia y Competitividad (Spain), under project #MTM2012-36740-c02-02. Professor Calabuig gratefully acknowledges the support of the Ministerio de Economia y Competitividad (Spain), under project #MTM2011-23164.Agud Albesa, L.; Calabuig Rodriguez, JM.; Sánchez Pérez, EA. (2015). On the smoothness of L p of a positive vector measure. Monatshefte für Mathematik. 178(3):329-343. https://doi.org/10.1007/s00605-014-0666-7S3293431783Beauzamy, B.: Introduction to Banach Spaces and Their Geometry. North-Holland, Amsterdam (1982)Diestel, J., Uhl, J.J.: Vector measures. In: Mathematical Surveys, vol. 15. AMS, Providence (1977)Fernández, A., Mayoral, F., Naranjo, F., Sáez, C., Sánchez-Pérez, E.A.: Spaces of p-integrable functions with respect to a vector measure. Positivity 10, 1–16 (2006)Ferrando, I., Rodríguez, J.: The weak topology on $$L^p$$ L p of a vector measure. Topol. Appl. 155(13), 1439–1444 (2008)Godefroy, G.: Boundaries of a convex set and interpolation sets. Math. Ann. 277(2), 173–184 (1987)Howard, R., Schep, A.R.: Norms of positive operators on $$L^p$$ L p -spaces. Proc. Am. Math. Soc. 109(1), 135–146 (1990)Lindenstrauss, J., Tzafriri, L.: Classical Banach Spaces II. Springer, Berlin (1977)Meyer-Nieberg, P.: Banach Latticces. Universitext, Springer-Verlag, Berlin (1991)Okada, S., Ricker, W.J., Sánchez-Pérez, E.A.: Optimal Domain and Integral Extension of Operators Acting in Function Spaces. Operator Theory: Advances and Applications, vol. 180. Birkhäuser Verlag, Basel (2008)Schep, A.: Products and factors of Banach function spaces. Positivity 14(2), 301–319 (2010

Differentiability of L-p of a vector measure and applications to the Bishop-Phelps-Bollobas property

[EN] We study the properties of Gâteaux, Fréchet, uniformly Fréchet and uniformly Gâteaux smoothness of the space Lp(m) of scalar p-integrable functions with respect to a positive vector measure m with values in a Banach lattice. Applications in the setting of the Bishop-Phelps-Bollobás property (both for operators and bilinear forms) are also given.Research supported by Ministerio de Economia y Competitividad and FEDER under projects MTM2012-36740-c02-02 (L. Agud and E.A. Sanchez-Perez), MTM201453009-P (J.M. Calabuig) and MTM2014-54182-P (S. Lajara). S. Lajara was also supported by project 19275/PI/14 funded by Fundacion Seneca-Agencia de Ciencia y Tecnologia de la Region de Murcia within the framework of PCTIRM 2011-2014.Agud Albesa, L.; Calabuig, JM.; Lajara, S.; Sánchez Pérez, EA. (2017). Differentiability of L-p of a vector measure and applications to the Bishop-Phelps-Bollobas property. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 111(3):735-751. https://doi.org/10.1007/s13398-016-0327-xS7357511113Acosta, M.D., Aron, R.M., García, D., Maestre, M.: The Bishop–Phelps–Bollobás theorem for operators. J. Funct. Anal. 254(11), 2780–2799 (2008)Acosta, M.D., Becerra-Guerrero, J., Choi, Y.S., García, D., Kim, S.K., Lee, H.J., Maestre, M.: The Bishop–Phelps–Bollobás theorem for bilinear forms and polinomials. J. Math. Soc. Jpn 66(3), 957–979 (2014)Acosta, M.D., Becerra-Guerrero, J., García, D., Maestre, M.: The Bishop–Phelps–Bollobás theorem for bilinear forms. Trans. Am. Math. Soc. 11, 5911–5932 (2013)Agud, L., Calabuig, J.M., Sánchez Pérez, E.A.: On the smoothness of $$L^p$$ L p of a positive vector measure. Monatsh. Math. 178(3), 329–343 (2015)Aron, R.M., Cascales, B., Kozhushkina, O.: The Bishop–Phelps–Bollobás theorem and Asplund operators. Proc. Am. Math. Soc. 139, 3553–3560 (2011)Bishop, E., Phelps, R.R.: A proof that every Banach space is subreflexive. Bull. Am. Math. Soc. 67, 97–98 (1961)Bollobás, B.: An extension to the theorem of Bishop and Phelps. Bull. Lond. Math. Soc. 2, 181–182 (1970)Cascales, B., Guirao, A.J., Kadets, V.: A Bishop–Phelps–Bollobás theorem type theorem for uniform algebras. Adv. Math. 240, 370–382 (2013)Choi, Y.S., Song, H.G.: The Bishop–Phelps–Bollobás theorem fails for bilinear forms on $$\ell _1\times \ell _1$$ ℓ 1 × ℓ 1 . J. Math. Anal. Appl. 360, 752–753 (2009)Deville, R., Godefroy, G., Zizler, V.: Smoothness and renormings in Banach spaces. Pitman Monographs and Surveys in Pure and Appl. Math., vol. 64, Longman, Harlow (1993)Diestel, J., Uhl, J.J.: Vector Measures. Math. Surveys, vol. 15, AMS, Providence, RI (1977)Fabian, M., Godefroy, G., Montesinos, V., Zizler, V.: Inner characterizations of weakly compactly generated Banach spaces and their relatives. J. Math. Anal. Appl. 297, 419–455 (2004)Fabian, M., Godefroy, G., Zizler, V.: The structure of uniformly Gâteaux smooth Banach spaces. Israel J. Math. 124, 243–252 (2001)Fabian, M., Habala, P., Hájek, P., Montesinos, V., Zizler, V.: Banach Space Theory: The Basis for Linear and Nonlinear Analysis. CMS Books in Mathematics, Springer, New York (2011)Fabian, M., Lajara, S.: Smooth renormings of the Lebesgue–Bochner function space $$L^1(\mu, X)$$ L 1 ( μ , X ) . Stud. Math. 209(3), 247–265 (2012)Ferrando, I., Rodríguez, J.: The weak topology on $$L^p$$ L p of a vector measure. Top. Appl. 155(13), 1439–1444 (2008)Hájek, P., Johanis, M.: Smooth analysis in Banach spaces. De Gruyter Series in Nonlinear Analysis and Applications, De Gruyter (2014)Kim, S.K.: The Bishop–Phelps–Bollobás theorem for operators from $$c_0$$ c 0 to uniformly convex spaces. Israel J. Math. 197, 425–435 (2013)Kim, S.K., Lee, H.J.: The Bishop–Phelps–Bollobás theorem for operators from $$C(K)$$ C ( K ) to uniformly convex spaces. J. Math. Anal. Appl. 421(1), 51–58 (2015)Hudzik, H., Kamińska, A., Mastylo, M.: Monotonocity and rotundity properties in Banach lattices. Rock. Mount J. Math. 30(3), 933–950 (2000)Kutzarova, D., Troyanski, S.L.: On equivalent norms which are uniformly convex or uniformly differentiable in every direction in symmetric function spaces. Serdica 11, 121–134 (1985)Okada, S., Ricker, W.J., Sánchez-Pérez, E.A.: Optimal Domain and Integral Extension of Operators Acting in Function Spaces. Operator Theory: Advances and Applications, vol. 180. Birkhäuser Verlag, Basel (2008

Staphylococcus aureus nasal colonization in Spanish children. The COSACO nationwide surveillance study

Objective: To assess the prevalence and risk factors for S. aureus and methicillin-resistant S. aureus (MRSA) nasal colonization in Spanish children. Methods: Cross-sectional study of patients <14 years from primary care centers all over Spain. Clinical data and nasal aspirates were collected from March to July 2018. Results: A total of 1876 patients were enrolled. Prevalence of S. aureus and MRSA colonization were 33% (95% CI 30.9–35.1) and 1.44% (95% CI 0.9–2), respectively. Thirtythree percent of the children (633/1876) presented chronic conditions, mainly atopic dermatitis, asthma and/or allergy (524/633). Factors associated with S. aureus colonization were age =5 years (OR 1.10, 95% CI 1.07–1.12), male sex (OR 1.43, 95% CI 1.17–1.76), urban setting (OR 1.46, 95% CI 1.08–1.97) and the presence of asthma, atopic dermatitis or allergies (OR 1.25; 95% CI: 1.093–1.43). Rural residence was the only factor associated with MRSA colonization (OR 3.62, 95% CI 1.57–8.36). MRSA was more frequently resistant than methicillin-susceptible S. aureus to ciprofloxacin [41.2% vs 2.6%; p<0.0001], clindamycin [26% vs 16.9%; p=0.39], and mupirocin [14.3% vs 6.7%; p=0.18]. None of the MRSA strains was resistant to tetracycline, fosfomycin, vancomycin or daptomycin. Conclusions: The main risk factors for S. aureus colonization in Spanish children are being above five years of age, male gender, atopic dermatitis, asthma or allergy, and residence in urban areas. MRSA colonization is low, but higher than in other European countries and is associated with rural settings

Characterization of methicillin-resistant Staphylococcus aureus strains colonizing the nostrils of Spanish children

Objective: To characterize the Staphylococcus aureus strains colonizing healthy Spanish children. Methods: Between March and July 2018, 1876 Spanish children younger than 14 years attending primary healthcare centers were recruited from rural and urban areas. Staphylococcus aureus colonization of the anterior nostrils was analyzed. MecA and mecC genes, antibiotic susceptibility, and genotyping according to the spa were determined in all strains, and the following toxins were examined: Panton-Valentine leucocidin (pvl), toxic shock syndrome toxin (tst), and exfoliative toxins (eta, etb, etd). Multilocus sequence typing (MLST) and staphylococcal cassette chromosome (SCCmec) typing were performed on methicillin-resistant Staphylococcus aureus (MRSA) strains, as well as pulsed-field gel electrophoresis (PFGE). Results: 619 strains were isolated in 1876 children (33%), and 92% of them were sent for characterization to the Spanish National Centre of Microbiology (n = 572). Twenty (3.5%) of these strains were mecA-positive. Several spa types were detected among MRSA, being t002 the most frequently observed (30%), associating with SCCmec IVc. Among MSSA, 33% were positive for tst, while only 0.73% were positive for pvl. The 20 MRSA strains were negative for pvl, and 6 (30%) harbored the tst gene. Conclusions: methicillin-resistant Staphylococcus aureus nasal colonization in Spanish children is rare, with t002 being the most observed spa type, associated with SCCmec IVc. None of the MRSA strains produced pvl, but up to 30% of S. aureus strains were positive for tst

Open questions in utility theory

Throughout this paper, our main idea is to explore different classical questions arising in Utility Theory, with a particular attention to those that lean on numerical representations of preference orderings. We intend to present a survey of open questions in that discipline, also showing the state-of-art of the corresponding literature.This work is partially supported by the research projects ECO2015-65031-R, MTM2015-63608-P (MINECO/ AEI-FEDER, UE), and TIN2016-77356-P (MINECO/ AEI-FEDER, UE)