Renormings and extremal structures

In this paper we use renorming techniques to settle several questions on extremal structures of Banach spaces. We construct a unitary vector in a dual space which is not a weak∧ -unitary. We construct an exposed point in the unit ball of a Banach space X that remains exposed in the unit ball of X(4) but is not extreme in the unit ball of X(6)

Pension disparities between men and women: which evolutions?

Mens and womens pensions and retirement ages remain very different, even if this gap has been closing (slowly) for the most recent generations. This work analyses possible developments till 2040. We first study the impact on future pension entitlements and on disparities between genders of the rise in womens participation in the labour market since the early 70s. Simulations carried out with the Destinie microsimulation model conclude that the gender gap keeps closing by the year 2040, essentially because of the rise in womens years of contribution. In a second part, we study the gender impact of pension reforms since the 90s. Although these reforms do not differentiate explicitly between genders, they can have diverging impacts for men and women due to interactions between the new rules and career profiles. Simulations show that this is actually the case. Without reforms, the ratio between pensions for men and women in the private sector would have fallen from 1,99 for cohorts 1940-44 to 1,47 for cohorts 1965-74. After reforms, the new ratio is expected to be 1,59. But the underlying mechanisms are very different from one reform to the next. The 1993 reform has the largest impact: computing the reference wage on the 25 rather than the 10 best years of ones career is more penalizing for women. The impact of the 2003 reform rather results from the fact that women make a larger use of new possibilities to retire before reaching the full rate. The relative reduction of their pension level is therefore the counterpart of an earlier age at benefit claiming. In the public sector, the same 2003 reform is a little more penalizing for men.Pension system, microsimulation, Destinie, pension reform, gender

On peak phenomena for non-commutative H∞H^\infty

A non-commutative extension of Amar and Lederer's peak set result is given. As its simple applications it is shown that any non-commutative $H^\infty$-algebra $H^\infty(M,\tau)$ has unique predual,and moreover some restriction in some of the results of Blecher and Labuschagne are removed, making them hold in full generality.Comment: final version (the presentation of some part is revised and one reference added

Renormings and extremal structures

Abstract. In this paper we use renorming techniques to settle several questions on extremal structures of Banach spaces. We construct a unitary vector in a dual space which is not a weak * -unitary. We construct an exposed point in the unit ball of a Banach space X that remains exposed in the unit ball of X (4) but is not extreme in the unit ball of X (6)

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

A remark on totally smooth renormings

[EN] E. Oja, T. Viil, andD. Werner showed, in Totally smooth renormings, Archiv der Mathematik, 112, 3, (2019), 269-281, that a weakly compactly generated Banach space ( X, center dot) with the property that every linear functional on X has a unique Hahn-Banach extension to the bidual X ** (the so-called Phelps' property U in X **, also known as the Hahn-Banach smoothness property) can be renormed to have the stronger property that for every subspace Y of X, every linear functional on Y has a unique Hahn-Banach extension to X ** (the so-called total smoothness property of the space). We mention here that this result holds in full generality -without any restriction on the space- and in a stronger form, thanks to a result ofM. Raja, On dual locally uniformly rotund norms, Israel Journal of Mathematics 129 (2002), 77-91.Supported by AEI/FEDER (project MTM2017-83262-C2-2-P of Ministerio de Economia y Competitividad), by Fundacion Seneca, Region de Murcia (Grant 19368/PI/14), and Universitat Politecnica de Valencia (A. J. Guirao). Supported by AEI/FEDER (project MTM2017-83262-C2-1-P of Ministerio de Economia y Competitividad) and Universitat Politecnica de Valencia (V. Montesinos). We thank the referees for their work, that neatly improved the original version of this note to its final form.Cobollo, C.; Guirao Sánchez, AJ.; Montesinos Santalucia, V. (2020). A remark on totally smooth renormings. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 114(2):1-4. https://doi.org/10.1007/s13398-020-00831-5S141142Fabian, M., Habala, P., Hájek, P., Montesinos, V., Zizler, V.: Banach space theory: the basis of linear and nonlinear analysis. Springer, New York (2011)Fabian, M., Montesinos, V., Zizler, V.: Smoothness in Banach spaces. Selected problems. Rev. R. Acad. Cien. Ser. A. Mat. RACSAM. 100(1–2), 101–125 (2006)Ferrari, S., Orihuela, J., Raja, M.: Generalized metric properties of spheres and renorming of Banach spaces. Rev. R. Acad. Cienc. Exactas Fis. Natl. Ser. A Math. RACSAM. 113, 2655–2663 (2019)Foguel, S.R.: On a theorem by A. E. Taylor. Proc. Amer. Math. Soc. 9, 325 (1958)Godefroy, G.: Points de Namioka, espaces normants, applications à la théorie isométrique de la dualité. Israel J. Math. 38, 209–220 (1981)Guirao, A.J., Montesinos, V., Zizler, V.: Open Problems in the geometry and analysis of Banach spaces. Springer International Pub, Switzerland (2016)Harmand, P., Werner, D., Werner, W.: M-ideals in Banach spaces and Banach algebras. Lecture notes in math, vol. 1547. Springer, Berlin (1993)Haydon, R.: Locally uniformly rotund norms in Banach spaces and their duals. J. Funct. Anal. 254, 2023–2039 (2008)Oja, E., Viil, T., Werner, D.: Totally smooth renormings. Archiv. der. Mathematik. 112(3), 269–281 (2019)Phelps, R.R.: Uniqueness of Hahn–Banach extensions and unique best approximation. Trans. Amer. Math. Soc. 95, 238–255 (1960)Raja, M.: On dual locally uniformly rotund norms. Israel J. Math. 129, 77–91 (2002)Smith, R.J., Troyanski, S.L.: Renormings of $$C(K)$$ spaces. Rev. R. Acad. Cienc. Exactas Fís. Natl. Ser. A Math. RACSAM 104(2), 375–412 (2010)Sullivan, F.: Geometrical properties determined by the higher duals of a Banach space. Illinois J. Math. 21, 315–331 (1977)Taylor, A.E.: The extension of linear functionals. Duke Math. J. 5, 538–547 (1939

Future perspectives on sustainable tribology

AbstractThis paper highlights the future perspectives of sustainable tribology by examining the economic, environmental and social impact of three tribological case studies. One case study examines the sustainability and durability of micro-CHP systems looking the tribological phenomena generated within a scroll expander system. The scroll is the main part of a specific micro-CHP system and experiences wear and cavitation damage. The tribological optimization of the scroll expander improves the sustainability of the micro-CHP unit while it has a serious economic and environmental impact to the consumers and to the society in general. Another case study is focused on friction and wear performance of lifeboat launch slipways. The causes of high friction and wear during the RNLI's lifeboat launches along an inclined slipway are investigated with a view to reducing the environmental impact due to slipway panel wear and lubricant release into the marine environment. The project encompasses the sustainable design of slipway panels using design modifications based on tribological investigations to double their lifespan, while environmental and economic impact was significantly reduced by the use of biodegradable greases and water as lubricants. The final case study involves an investigation of recycled plastic materials to replace polyurethane used on skateboard wheels, scooters and similar applications. Polyurethane (PU) is difficult to recycle. With the dwindling resources and environmental problems facing the world today, recycling for both waste reduction and resource preservation has become an increasingly important aspect of sustainability. The tribological results showed that recycled polycarbonate plastic can effectively act as a substitute to polyurethane wheels. Moreover, sustainability considerations showing the environmental benefits of the use of recycled plastics over PU include reducing the CO2 footprint by 50% and the energy consumed by 60%, among other benefits. These case studies emphasise the importance of sustainable tribology in our epoch showing that increased sustainability performance can be achieved through tribology to a significant extent in many cases, providing stability to our world and more viable long term growth to our societies

The impact of four years of semiannual treatments with albendazole alone on lymphatic filariasis and soil-transmitted helminth infections: A community-based study in the Democratic Republic of the Congo

BACKGROUND: The World Health Organization now recommends semiannual mass drug administration (MDA) of albendazole with integrated vector management as an option for eliminating lymphatic filariasis (LF) in areas of loiasis-endemic countries where it may not be safe to use diethylcarbamazine or ivermectin in MDA programs. However, the published evidence base to support this policy is thin, and uptake by national programs has been slow. METHODOLOGY/PRINCIPAL FINDINGS: We conducted a community trial to assess the impact of semiannual MDA on lymphatic filariasis and soil-transmitted helminth infections (STH) in two villages in the Bandundu province of the Democratic Republic of the Congo with moderately high prevalences for LF and hookworm infections. MDA with albendazole was provided every six months from June 2014 to December 2017 with treatment coverages of the eligible population (all ≥ 2 year of age) that ranged between 56% and 88%. No adverse effects were reported during the trial. Evaluation at 48 months, (i.e. 6 months after the 8th round of MDA), showed that W. bancrofti microfilaremia (Mf) prevalence in the study communities had decreased between 2014 to 2018 from 12% to 0.9% (p\u3c0.001). The prevalence of W. bancrofti antigenemia was also significantly reduced from 31.6% to 8.5% (p\u3c0.001). MDA with albendazole also reduced hookworm, Ascaris lumbricoides and Trichuris trichiura infection prevalences in the community from 58.6% to 21.2% (p\u3c0.001), from 14.0% to 1.6% and 4.1% to 2.9%, respectively. Hookworm and Ascaris infection intensities were reduced by 93% (p = 0.02) and 57% (p = 0.03), respectively. In contrast, Trichuris infection intensity was not significantly reduced by MDA (p = 0.61) over this time period. CONCLUSION/SIGNIFICANCE: These results provide strong evidence that semiannual MDA with albendazole alone is a safe and effective strategy for LF elimination in Central Africa. Community MDA also had a major impact on STH infections