Mean ergodicity and spectrum of the Cesàro operator on weighted c0 spaces

[EN] A detailed investigation is made of the continuity, the compactness and the spectrum of the Cesàro operator C acting on the weighted Banach sequence space c0(w) for a bounded, strictly positive weight w. New features arise in the weighted setting (e.g. existence of eigenvalues, compactness, mean ergodicity) which are not present in the classical setting of c0.The research of the first two authors was partially supported by the Projects MTM2013-43540-P, GVA Prometeo II/2013/013 and ACOMP/2015/186 (Spain).Albanese, AA.; Bonet Solves, JA.; Ricker, WJ. (2016). Mean ergodicity and spectrum of the Cesàro operator on weighted c0 spaces. Positivity. 20:761-803. https://doi.org/10.1007/s11117-015-0385-xS76180320Akhmedov, A.M., Başar, F.: On the fine spectrum of the Cesàro operator in $$c_0$$ c 0 . Math. J. Ibaraki Univ. 36, 25–32 (2004)Akhmedov, A.M., Başar, F.: The fine spectrum of the Cesàro operator $$C_1$$ C 1 over the sequence space $$bv_p, (1 \le p < \infty )$$ b v p , ( 1 ≤ p < ∞ ) . Math. J. Okayama Univ. 50, 135–147 (2008)Albanese, A.A., Bonet, J., Ricker, W.J.: Convergence of arithmetic means of operators in Fréchet spaces. J. Math. Anal. Appl. 401, 160–173 (2013)Albanese, A.A., Bonet, J., Ricker, W.J.: Spectrum and compactness of the Cesàro operator on weighted $$\ell _p$$ ℓ p spaces. J. Aust. Math. Soc. 99, 287–314 (2015)Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator in the Fréchet spaces $$\ell ^{p+}$$ ℓ p + and $$L ^{p-}$$ L p - . Glasg. Math. J (to appear)Ansari, S.I., Bourdon, P.S.: Some properties of cyclic operators. Acta Sci. Math. Szeged 63, 195–207 (1997)Brown, A., Halmos, P.R., Shields, A.L.: Cesàro operators. Acta Sci. Math. Szeged 26, 125–137 (1965)Curbera, G.P., Ricker, W.J.: Spectrum of the Cesàro operator in $$\ell ^p$$ ℓ p . Arch. Math. 100, 267–271 (2013)Curbera, G.P., Ricker, W.J.: Solid extensions of the Cesàro operator on $$\ell ^p$$ ℓ p and $$c_0$$ c 0 . Integr. Equ. Oper. Theory 80, 61–77 (2014)Curbera, G.P., Ricker, W.J.: The Cesàro operator and unconditional Taylor series in Hardy spaces. Integr. Equ. Oper. Theory 83, 179–195 (2015)Diestel, J.: Sequences and Series in Banach Spaces. Springer, New York (1984)Dowson, H.R.: Spectral Theory of Linear Operators. Academic Press, London (1978)Dunford, N., Schwartz, J.T.: Linear Operators I: General Theory, 2nd Printing. Wiley Interscience Publ, New York (1964)Emilion, R.: Mean-bounded operators and mean ergodic theorems. J. Funct. Anal. 61, 1–14 (1985)Goldberg, S.: Unbounded Linear Operators: Theory and Applications. Dover Publ, New York (1985)Hille, E.: Remarks on ergodic theorems. Trans. Am. Math. Soc. 57, 246–269 (1945)Jarchow, H.: Locally Convex Spaces. Teubner, Stuttgart (1981)Krengel, U.: Ergodic Theorems. de Gruyter, Berlin (1985)Leibowitz, G.: Spectra of discrete Cesàro operators. Tamkang J. Math. 3, 123–132 (1972)Lin, M.: On the uniform ergodic theorem. Proc. Am. Math. Soc. 43, 337–340 (1974)Megginson, R.E.: An Introduction to Banach Space Theory. Springer, New York (1998)Mureşan, M.: A Concrete Approach to Classical Analysis. Springer, Berlin (2008)Okutoyi, J.I.: On the spectrum of $$C_1$$ C 1 as an operator on $$bv_0$$ b v 0 . J. Aust. Math. Soc. Ser. A 48, 79–86 (1990)Radjavi, H., Tam, P.-W., Tan, K.-K.: Mean ergodicity for compact operators. Studia Math. 158, 207–217 (2003)Reade, J.B.: On the spectrum of the Cesàro operator. Bull. Lond. Math. Soc. 17, 263–267 (1985)Rhoades, B.E., Yildirim, M.: The spectra and fine spectra of factorable matrices on $$c_0$$ c 0 . Math. Commun. 16, 265–270 (2011)Taylor, A.E.: Introduction to Functional Analysis. Wiley, New York (1958

Metabolomic Analysis in Severe Childhood Pneumonia in The Gambia, West Africa: Findings from a Pilot Study

Pneumonia remains the leading cause of death in young children globally and improved diagnostics are needed to better identify cases and reduce case fatality. Metabolomics, a rapidly evolving field aimed at characterizing metabolites in biofluids, has the potential to improve diagnostics in a range of diseases. The objective of this pilot study is to apply metabolomic analysis to childhood pneumonia to explore its potential to improve pneumonia diagnosis in a high-burden setting. and Random Forests (RF). ‘Unsupervised’ (blinded) data were analyzed by Principal Component Analysis (PCA), while ‘supervised’ (unblinded) analysis was by Partial Least Squares-Discriminant Analysis (PLS-DA) and Orthogonal Projection to Latent Structures (OPLS). Potential markers were extracted from S-plots constructed following analysis with OPLS, and markers were chosen based on their contribution to the variation and correlation within the data set. The dataset was additionally analyzed with the machine-learning algorithm RF in order to address issues of model overfitting and markers were selected based on their variable importance ranking. Unsupervised PCA analysis revealed good separation of pneumonia and control groups, with even clearer separation of the groups with PLS-DA and OPLS analysis. Statistically significant differences (p<0.05) between groups were seen with the following metabolites: uric acid, hypoxanthine and glutamic acid were higher in plasma from cases, while L-tryptophan and adenosine-5′-diphosphate (ADP) were lower; uric acid and L-histidine were lower in urine from cases. The key limitation of this study is its small size.Metabolomic analysis clearly distinguished severe pneumonia patients from community controls. The metabolites identified are important for the host response to infection through antioxidant, inflammatory and antimicrobial pathways, and energy metabolism. Larger studies are needed to determine whether these findings are pneumonia-specific and to distinguish organism-specific responses. Metabolomics has considerable potential to improve diagnostics for childhood pneumonia

Clinical chronobiology: a timely consideration in critical care medicine

A fundamental aspect of human physiology is its cyclical nature over a 24-h period, a feature conserved across most life on Earth. Organisms compartmentalise processes with respect to time in order to promote survival, in a manner that mirrors the rotation of the planet and accompanying diurnal cycles of light and darkness. The influence of circadian rhythms can no longer be overlooked in clinical settings; this review provides intensivists with an up-to-date understanding of the burgeoning field of chronobiology, and suggests ways to incorporate these concepts into daily practice to improve patient outcomes. We outline the function of molecular clocks in remote tissues, which adjust cellular and global physiological function according to the time of day, and the potential clinical advantages to keeping in time with them. We highlight the consequences of "chronopathology", when this harmony is lost, and the risk factors for this condition in critically ill patients. We introduce the concept of "chronofitness" as a new target in the treatment of critical illness: preserving the internal synchronisation of clocks in different tissues, as well as external synchronisation with the environment. We describe methods for monitoring circadian rhythms in a clinical setting, and how this technology may be used for identifying optimal time windows for interventions, or to alert the physician to a critical deterioration of circadian rhythmicity. We suggest a chronobiological approach to critical illness, involving multicomponent strategies to promote chronofitness (chronobundles), and further investment in the development of personalised, time-based treatment for critically ill patients

Consensus guidelines for the use and interpretation of angiogenesis assays

The formation of new blood vessels, or angiogenesis, is a complex process that plays important roles in growth and development, tissue and organ regeneration, as well as numerous pathological conditions. Angiogenesis undergoes multiple discrete steps that can be individually evaluated and quantified by a large number of bioassays. These independent assessments hold advantages but also have limitations. This article describes in vivo, ex vivo, and in vitro bioassays that are available for the evaluation of angiogenesis and highlights critical aspects that are relevant for their execution and proper interpretation. As such, this collaborative work is the first edition of consensus guidelines on angiogenesis bioassays to serve for current and future reference

Prevention of acute kidney injury and protection of renal function in the intensive care unit

Acute renal failure on the intensive care unit is associated with significant mortality and morbidity. To determine recommendations for the prevention of acute kidney injury (AKI), focusing on the role of potential preventative maneuvers including volume expansion, diuretics, use of inotropes, vasopressors/vasodilators, hormonal interventions, nutrition, and extracorporeal techniques. A systematic search of the literature was performed for studies using these potential protective agents in adult patients at risk for acute renal failure/kidney injury between 1966 and 2009. The following clinical conditions were considered: major surgery, critical illness, sepsis, shock, and use of potentially nephrotoxic drugs and radiocontrast media. Where possible the following endpoints were extracted: creatinine clearance, glomerular filtration rate, increase in serum creatinine, urine output, and markers of tubular injury. Clinical endpoints included the need for renal replacement therapy, length of stay, and mortality. Studies are graded according to the international Grades of Recommendation, Assessment, Development, and Evaluation (GRADE) group system Several measures are recommended, though none carries grade 1A. We recommend prompt resuscitation of the circulation with special attention to providing adequate hydration whilst avoiding high-molecular-weight hydroxy-ethyl starch (HES) preparations, maintaining adequate blood pressure using vasopressors in vasodilatory shock. We suggest using vasopressors in vasodilatory hypotension, specific vasodilators under strict hemodynamic control, sodium bicarbonate for emergency procedures administering contrast media, and periprocedural hemofiltration in severe chronic renal insufficiency undergoing coronary intervention

Australian experience with frozen blood products on military operations

Historically, the Australian Defence Force (ADF) has sourced all its blood supplies from the Australian Red Cross Blood Service. Recent ADF operations in the Middle East have highlighted a need to rely on other nations' blood supply systems. In 2008, the ADF embedded a surgical and intensive care team into the Netherlands-led forward health facility at the Uruzgan Medical Centre at Tarin Kowt in Afghanistan. To date, three teams have provided 2-month rotations as part of the North Atlantic Treaty Organization International Security Assistance Force in Afghanistan. The Netherlands armed forces use a sophisticated system for supply of liquid and frozen blood products (frozen red cells, plasma and platelets). We review Australian experience with the Dutch system of supplying blood products for major trauma resuscitation in Afghanistan.Neuhaus Susan J., Wishaw Ken and Lelkens Charleshttp://cat.inist.fr/?aModele=afficheN&cpsidt=2244618