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

Analysis of Italian isolates of Pantoea stewartii subsp. stewartii and development of a real-time PCR-based diagnostic method

Pantoea stewartii subsp. stewartii (Pss) causes Stewart's vascular wilt of maize, and it is responsible for serious crop losses. Pss is indigenous to North America and spreads with maize seeds. The presence of Pss has been notified in Italy since 2015. The risk assessment of the entry of Pss in the EU from the United States through seed trade is in the order of magnitude of hundred introductions per year. Several molecular or serological tests were developed for the detection of Pss and used as official analysis for the certification of commercial seeds. However, some of these tests lack adequate specificity, not allowing to correctly discriminate Pss from P. stewartii subsp. indologenes (Psi). Psi is occasionally present in maize seeds and is avirulent for maize. In this study, several Italian isolates of Pss recovered in 2015 and 2018 have been characterized by molecular, biochemical, and pathogenicity tests; moreover, their genomes have been assembled through MinION and Illumina-sequencing procedures. Genomic analysis reveals multiple introgression events. Exploiting these results, a new primer combination has been defined and verified by real-time PCR, allowing the development of a specific molecular test able to detect the presence of Pss down to the concentration of 103  CFU/ml in spiked samples of maize seed extracts. Due to the high analytical sensitivity and specificity achieved with this test, the detection of Pss has been improved disentangling the inconclusive results in Pss maize seed diagnosis, overcoming its misidentification in place of Psi. Altogether, this test addresses the critical issue associated with maize seeds imported from regions where Stewart's disease is endemic

Symptomatic nonconvulsive status epilepticus erroneously suggestive of sporadic Creutzfeldt-Jakob disease

Nonconvulsive status epilepticus (NCSE) may have heterogeneous presentations and differential diagnosis may be particularly difficult because clinical signs coupled with periodic EEG pattern are most often subtle or non-specific. Moreover, few cases of NCSE have been previously described as the presenting symptom of sporadic Creutzfeldt–Jakob disease (sCJD) [1,4,5,7]. We describe a patient with a NCSE strongly, but erroneously, suggestive of a probable sCJD

Cranio-Mandibular Disorders after Whiplash Injury: A Mono-Institutional Clinical Study on 31 Patients

Background: Whiplash is a consequence of traumatic injuries, mostly related to road accidents, with variable clinical manifestations, also known as Whiplash Associated Disorders, such as neck, head and temporo-cranio-mandibular pain. Methods: The current study aims to evaluate the onset and evolution of temporomandibular joint pain in people with whiplash in a study group treated with the use of Zimmer Collars (adjustable rigid cervical collars for neck immobilization), as compared to a control group. This prospective study included 31 patients followed by the Dental Prosthesis Department of the University of Bari “Aldo Moro”: 20 patients with whiplash (age range: 20–39 years) treated with Zimmer collars and 11 patients with whiplash (age range: 20–33 years) who were not. Immediately after the whiplash occurred, a visual analogue scale (VAS) was used to describe the intensity of pain and to complete the chart of the European Academy of Craniomandibular Disorders. Five out of twenty patients, already treated with a Zimmer collar, wore an occlusal splint as well because of persistent pain reported at the 28-day and 60-day follow-up and were supported by pharmacological therapy with analgesics (paracetamol) and muscle relaxants (thiocolchicoside). Results: During the last follow-up (at six months), three out of five patients displayed a residual VAS score of 3, 4, and 5, respectively, while the remaining two displayed a VAS of 0. In the control group, four out of eleven patients needed to wear an occlusal splint but without muscle relaxants and analgesics pharmacological therapy; these four corresponded to the patients showing a residual painful symptomatology, with VAS reaching value of 2, and also were the oldest patients of the group. Data regarding VAS values and Zimmer collar use, both at the first visit and six months later, were statistically analyzed. Conclusion: Our prospective study highlights how whiplash-associated acute disorders are often self-limiting over a period of few months, thus reducing the possibility of symptom chronicity; the latter seems to be strictly related to lesion severity, pre-existence of a craniomandibular dysfunction and patient age, but appears to be independent from Zimmer collar use, as statistically confirmed

Human papillomavirus infection is not related with prostatitis-related symptoms: results from a casecontrol study.

PurposeTo investigate the relationship between human papillomavirus (HPV) infection and prostatitis-related symptoms.Materials and MethodsAll young heterosexual patients with prostatitis-related symptoms attending the same Center from January 2005 to December 2010 were eligible for this case-control study. Sexually active asymptomatic men were considered as the control group. All subjects underwent clinical examination, Meares-Stamey test and DNA-HPV test. Patients with prostatitis-related symptoms and asymptomatic men were compared in terms of HPV prevalence. Moreover, multivariable Cox proportional hazards regression analysis was performed to determine the association between HPV infection and prostatitis-related symptoms.ResultsOverall, 814 out of 2,938 patients (27.7%) and 292 out of 1,081 controls (27.0%) proved positive to HPV. The HPV genotype distribution was as follows: HR-HPV 478 (43.3%), PHR-HPV 77 (6.9%), LR-HPV 187 (16.9%) and PNG-HPV 364 (32.9%). The most common HPV genotypes were: 6, 11, 16, 26, 51, 53 and 81. No difference was found between the two groups in terms of HPV infection (OR 1.03; 95% CI 0.88-1.22; p = 0.66). We noted a statistically significant increase in HPV infection over the period 2005 to 2010 (p < 0.001) in both groups. Moreover, we found a statistically significant increase in HPV 16 frequency from 2005 to 2010 (p = 0.002).ConclusionsThis study highlights that prostatitis-like symptoms are unrelated to HPV infection. Secondary, we highlight the high prevalence of asymptomatic HPV infection among young heterosexual men

Human papillomavirus infection is not related with prostatitis-related symptoms: results from a casecontrol study.

This study highlights that prostatitis-like symptoms are unrelated to HPV infection. Secondary, we highlight the high prevalence of asymptomatic HPV infection among young heterosexual men

On the flux phase conjecture at half-filling: an improved proof

We present a simplification of Lieb's proof of the flux phase conjecture for interacting fermion systems -- such as the Hubbard model --, at half filling on a general class of graphs. The main ingredient is a procedure which transforms a class of fermionic Hamiltonians into reflection positive form. The method can also be applied to other problems, which we briefly illustrate with two examples concerning the $t-V$ model and an extended Falicov-Kimball model.Comment: 23 pages, Latex, uses epsf.sty to include 3 eps figures, to appear in J. Stat. Phys., Dec. 199

Dose-volumerelated dysphagia after constrictor muscles definition in head and neck cancer intensitymodulated radiation treatment

OBJECTIVE: Dysphagia remains a side effect influencing the quality of life of patients with head and neck cancer (HNC) after radiotherapy. We evaluated the relationship between planned dose involvement and acute and late dysphagia in patients with HNC treated with intensity-modulated radiation therapy (IMRT), after a recontouring of constrictor muscles (PCs) and the cricopharyngeal muscle (CM). METHODS: Between December 2011 and December 2013, 56 patients with histologically proven HNC were treated with IMRT or volumetric-modulated arc therapy. The PCs and CM were recontoured. Correlations between acute and late toxicity and dosimetric parameters were evaluated. End points were analysed using univariate logistic regression. RESULTS: An increasing risk to develop acute dysphagia was observed when constraints to the middle PCs were not respected [mean dose (D(mean)) ≥50 Gy, maximum dose (D(max)) >60 Gy, V50 >70% with a p = 0.05]. The superior PC was not correlated with acute toxicity but only with late dysphagia. The inferior PC was not correlated with dysphagia; for the CM only, D(max) >60 Gy was correlated with acute dysphagia ≥ grade 2. CONCLUSION: According to our analysis, the superior PC has a major role, being correlated with dysphagia at 3 and 6 months after treatments; the middle PC maintains this correlation only at 3 months from the beginning of radiotherapy, but it does not have influence on late dysphagia. The inferior PC and CM have a minimum impact on swallowing symptoms. ADVANCES IN KNOWLEDGE: We used recent guidelines to define dose constraints of the PCs and CM. Two results emerge in the present analysis: the superior PC influences late dysphagia, while the middle PC influences acute dysphagia

Differential occurrence of S100A7 in breast cancer tissues: A proteomic-based investigation

PURPOSE: The present study reports for the first time a large-scale proteomic screening of the occurrence, subcellular localization and relative quantification of the S100A7 protein among a group of 100 patients, clinically grouped for the diagnosis of infiltrating ductal carcinoma (IDC). EXPERIMENTAL DESIGN: To this purpose, the methods of differential proteomics, Western blotting, and immunohistochemistry were used. RESULTS: The identity of two isoforms of the protein was assessed by mass spectrometry and immunologically confirmed. Moreover, we proved by immunocytochemical applications the exclusive localization of the protein within the neoplastic cells. The correlation of S100A7 expression levels with the collective profile of cancer patients' proteomics predicted functional interactions, distinct for the two isoforms. The S100A7b isoform was significantly correlated with specific protein clusters (calcium binding, signaling and cell motion, heat shock and folding) and intercrossing pathways (antioxidant, metabolic and apoptotic pathways), while the more acidic isoform was correlated with a narrow number of proteins mainly unrelated to the b isoform. CONCLUSIONS AND CLINICAL RELEVANCE: This study is the first proteomic-based report on S100A7 in a large series of IDC patients. The correlation with in silico data may significantly contribute the knowledge of possible pathways for S100A7, providing novel insights into the mechanism of action of this protein. We suggest that each S100A7 isoform is involved in critical phases of the breast cancer growth and progression, probably through interaction with different partner proteins