On the continuous Cesàro operator in certain function spaces

“The final publication is available at Springer via http://dx.doi.org/10.1007/s11117-014-0321-5"Various properties of the (continuous) Cesàro operator C, acting on Banach and Fréchet spaces of continuous functions and L p-spaces, are investigated. For instance, the spectrum and point spectrum of C are completely determined and a study of certain dynamics of C is undertaken (eg. hyper- and supercyclicity, chaotic behaviour). In addition, the mean (and uniform mean) ergodic nature of C acting in the various spaces is identified.The research of the first two authors was partially supported by the projects MTM2010-15200 and GVA Prometeo II/2013/013 (Spain). The second author gratefully acknowledges the support of the Alexander von Humboldt Foundation.Albanese, AA.; Bonet Solves, JA.; Ricker, WJ. (2015). On the continuous Cesàro operator in certain function spaces. Positivity. 19:659-679. https://doi.org/10.1007/s11117-014-0321-5S65967919Albanese, A.A.: Primary products of Banach spaces. Arch. Math. 66, 397–405 (1996)Albanese, A.A.: On subspaces of the spaces $$L^p_{\rm loc}$$ L loc p and of their strong duals. Math. Nachr. 197, 5–18 (1999)Albanese, A.A., Moscatelli, V.B.: Complemented subspaces of sums and products of copies of $$L^1 [0,1]$$ L 1 [ 0 , 1 ] . Rev. Mat. Univ. Complut. Madr. 9, 275–287 (1996)Albanese, A.A., Bonet, J., Ricker, W.J.: Mean ergodic operators in Fréchet spaces. Ann. Acad. Sci. Fenn. Math. 34, 401–436 (2009)Albanese, A.A., Bonet, J., Ricker, W.J.: On mean ergodic operators. In: Curbera, G.P. (eds.) Vector Measures, Integration and Related Topics. Operator Theory: Advances and Applications, vol. 201, pp. 1–20. Birkhäuser, Basel (2010)Albanese, A.A., Bonet, J., Ricker, W.J.: $$C_0$$ C 0 -semigroups and mean ergodic operators in a class of Fréchet spaces. J. Math. Anal. Appl. 365, 142–157 (2010)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)Bayart, F., Matheron, E.: Dynamics of linear operators. Cambridge Tracts in Mathematics, vol. 179. Cambridge University Press, Cambridge (2009)Bellenot, S.F., Dubinsky, E.: Fréchet spaces with nuclear Köthe quotients. Trans. Am. Math. Soc. 273, 579–594 (1982)Bonet, J., Frerick, L., Peris, A., Wengenroth, J.: Transitive and hypercyclic operators on locally convex spaces. Bull. Lond. Math. Soc. 37, 254–264 (2005)Boyd, D.W.: The spectrum of the Cesàro operator. Acta Sci. Math. (Szeged) 29, 31–34 (1968)Brown, A., Halmos, P.R., Shields, A.L.: Cesàro operators. Acta Sci. Math. (Szeged) 26, 125–137 (1965)Dierolf, S., Zarnadze, D.N.: A note on strictly regular Fréchet spaces. Arch. Math. 42, 549–556 (1984)Dunford, N., Schwartz, J.T.: Linear Operators I: General Theory (2nd Printing). Wiley-Interscience, New York (1964)Galaz Fontes, F., Solís, F.J.: Iterating the Cesàro operators. Proc. Am. Math. Soc. 136, 2147–2153 (2008)Galaz Fontes, F., Ruiz-Aguilar, R.W.: Grados de ciclicidad de los operadores de Cesàro–Hardy. Misc. Mat. 57, 103–117 (2013)González, M., León-Saavedra, F.: Cyclic behaviour of the Cesàro operator on $$L_2(0,+\infty )$$ L 2 ( 0 , + ∞ ) . Proc. Am. Math. Soc. 137, 2049–2055 (2009)Grosse-Erdmann, K.G., Peris Manguillot, A.: Linear chaos. In: Universitext. Springer, London (2011)Hardy, G.H., Littlewood, J.E., Pólya, G.: Inequalities. In: Reprint of the 1952 Edition. Cambridge Mathematical Library. Cambridge University Press, Cambridge (1988)Krengel, U.: Ergodic theorems. In: De Gruyter Studies in Mathematics, vol. 6. Walter de Gruyter Co., Berlin (1985)Leibowitz, G.M.: Spectra of finite range Cesàro operators. Acta Sci. Math. (Szeged) 35, 27–28 (1973)Leibowitz, G.M.: The Cesàro operators and their generalizations: examples in infinite-dimensional linear analysis. Am. Math. Mon. 80, 654–661 (1973)León-Saavedra, F., Piqueras-Lerena, A., Seoane-Sepúlveda, J.B.: Orbits of Cesàro type operators. Math. Nachr. 282, 764–773 (2009)Lin, M.: On the uniform ergodic theorem. Proc. Am. Math. Soc. 43, 337–340 (1974)Meise, R., Vogt, D.: Introduction to functional analysis. In: Oxford Graduate Texts in Mathematics, vol. 2. The Clarendon Press; Oxford University Press, New York (1997)Metafune, G., Moscatelli, V.B.: Quojections and prequojections. In: Terzioğlu, T. (ed.) Advances in the Theory of Fréchet spaces. NATO ASI Series, vol. 287, pp. 235–254. Kluwer Academic Publishers, Dordrecht (1989)Moscatelli, V.B.: Fréchet spaces without norms and without bases. Bull. Lond. Math. Soc. 12, 63–66 (1980)Piszczek, K.: Quasi-reflexive Fréchet spaces and mean ergodicity. J. Math. Anal. Appl. 361, 224–233 (2010)Piszczek, K.: Barrelled spaces and mean ergodicity. Rev R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 104, 5–11 (2010)Yosida, K.: Functional Analysis, 6th edn. Springer, Berlin (1980

Resident physician and hospital pharmacist familiarity with patient discharge medication costs

Objective Cost-related medication non-adherence is associated with increased health-care resource utilization and poor patient outcomes. Physicians-in-training generally receive little education regarding costs of prescribed therapy and may rely on hospital pharmacists for this information. However, little is documented regarding either of these health care providers’ familiarity with out-of pocket medication expenses borne by patients in the community. The purpose of this study was to evaluate and compare resident physician and hospital pharmacist familiarity with what patients pay for medications prescribed once discharged. Setting A major tertiary patient care and medical teaching centre in Canada. Method Internal medicine residents and hospital pharmacists within a specific health care organization were invited to participate in an online survey. Eight patient case scenarios and associated discharge therapeutic regimens were outlined and respondents asked to identify the costs patients would incur when having the prescription filled once discharged. Main Outcome Measure Total number and proportion of estimates above and below actual cost were calculated and compared between the groups using χ2 tests. Responses ±10% of the true cost were considered correct. Mean absolute values and standard deviation estimated costs, as well as cost increments above and below 10%, were calculated to assess the magnitude of the discrepancy between the respondent estimates and the actual total cost. Results Forty-four percent of physician residents and 26% of hospital pharmacists accessed the survey. Overall 39% and 47% of medication costs were under-estimated, 32% and 33% were overestimated, and 29% and 21% were correctly estimated by residents and pharmacists, respectively (P = NS). Incorrect estimates were evident across all therapeutic classes and medical indications presented in the survey. The greatest absolute cost discrepancy for both groups was under-estimation of linezolid ($800 and$400) and over-estimation of clopidogrel ($80) and bisoprolol therapy ($22) by residents and pharmacists, respectively. Conclusion Resident physicians and hospital pharmacists are unfamiliar with what patients must pay for drug therapy once discharged

Limited Awareness and Low Immediate Uptake of Pre-Exposure Prophylaxis among Men Who Have Sex with Men Using an Internet Social Networking Site

Background: In 2010, the iPrEx trial demonstrated that oral antiretroviral pre-exposure prophylaxis (PrEP) reduced the risk of HIV acquisition among high-risk men who have sex with men (MSM). The impact of iPrEx on PrEP knowledge and actual use among at-risk MSM is unknown. Online surveys were conducted to assess PrEP awareness, interest and experience among at-risk MSM before and after iPrEx, and to determine demographic and behavioral factors associated with these measures. Methods and Findings: Cross-sectional, national, internet-based surveys were administered to U.S. based members of the most popular American MSM social networking site 2 months before (n = 398) and 1 month after (n = 4 558) publication of iPrEx results. Comparisons were made between these samples with regards to PrEP knowledge, interest, and experience. Data were collected on demographics, sexual risk, and experience with post-exposure prophylaxis (PEP). Regression analyses were performed to identify factors associated with PrEP awareness, interest, and experience post-iPrEx. Most participants were white, educated, and indicated high-risk sexual behaviors. Awareness of PrEP was limited pre- and post-iPrEx (13% vs. 19%), whereas interest levels after being provided with a description of PrEP remained high (76% vs. 79%). PrEP use remained uncommon (0.7% vs. 0.9%). PrEP use was associated with PEP awareness (OR 7.46; CI 1.52–36.6) and PEP experience (OR 34.2; CI 13.3–88.4). PrEP interest was associated with older age (OR 1.01; CI 1.00–1.02), unprotected anal intercourse with ≥1 male partner in the prior 3 months (OR 1.40; CI 1.10–1.77), and perceiving oneself at increased risk for HIV acquisition (OR 1.20; CI 1.13–1.27). Conclusions: Among MSM engaged in online networking, awareness of PrEP was limited 1 month after the iPrEx data were released. Utilization was low, although some MSM who reported high-risk behaviors were interested in using PrEP. Studies are needed to understand barriers to PrEP utilization by at-risk MSM

Serotonin transporter binding of [123I]ADAM in bulimic women, their healthy twin sisters, and healthy women: a SPET study

<p>Abstract</p> <p>Background</p> <p>Bulimia Nervosa (BN) is believed to be caused by an interaction of genetic and environmental factors. Previous studies support the existence of a bulimia-related endophenotype as well as disturbances in serotonin (5-HT) transmission. We studied serotonin transporter (SERT) binding in BN, and to investigate the possibility of a SERT-related endophenotype for BN, did this in a sample of female twins. We hypothesized clearly reduced SERT binding in BN women as opposed to healthy women, and intermediate SERT binding in unaffected co-twins.</p> <p>Methods</p> <p>We studied 13 female twins with BN (9 with purging and 4 with non-purging BN) and 25 healthy women, including 6 healthy twin sisters of BN patients and 19 women from 10 healthy twin pairs. [¹²³I]ADAM, a selective SERT radioligand for single photon emission tomography (SPET) imaging, was used to assess SERT availability in the midbrain and the thalamus.</p> <p>Results</p> <p>No differences in SERT binding were evident when comparing the BN women, their unaffected co-twins and the healthy controls (p = 0.14). The healthy sisters of the BN patients and the healthy control women had similar SERT binding in both brain regions. In a <it>post hoc </it>subgroup analysis, the purging bulimics had higher SERT binding than the healthy women in the midbrain (p = 0.03), but not in the thalamus.</p> <p>Conclusion</p> <p>Our finding of increased SERT binding in the midbrain in the purging BN women raises the possibility that this subgroup of bulimics might differ in serotonergic function from the non-purging ones. The similarity of the unaffected co-twins and the healthy controls doesn't support our initial assumption of a SERT-related endophenotype for BN. Due to the small sample size, our results need to be interpreted with caution and verified in a larger sample.</p

Evidence-based Kernels: Fundamental Units of Behavioral Influence

This paper describes evidence-based kernels, fundamental units of behavioral influence that appear to underlie effective prevention and treatment for children, adults, and families. A kernel is a behavior–influence procedure shown through experimental analysis to affect a specific behavior and that is indivisible in the sense that removing any of its components would render it inert. Existing evidence shows that a variety of kernels can influence behavior in context, and some evidence suggests that frequent use or sufficient use of some kernels may produce longer lasting behavioral shifts. The analysis of kernels could contribute to an empirically based theory of behavioral influence, augment existing prevention or treatment efforts, facilitate the dissemination of effective prevention and treatment practices, clarify the active ingredients in existing interventions, and contribute to efficiently developing interventions that are more effective. Kernels involve one or more of the following mechanisms of behavior influence: reinforcement, altering antecedents, changing verbal relational responding, or changing physiological states directly. The paper describes 52 of these kernels, and details practical, theoretical, and research implications, including calling for a national database of kernels that influence human behavior