A proof of uniqueness of the Gurarii space

We present a short and elementary proof of isometric uniqueness of the Gurarii space.Comment: 6 pages, some improvements incorporate

A note on completeness of weighted normed spaces of analytic functions

[EN] Given a non-negative weight v, not necessarily bounded or strictly positive, defined on a domain G in the complex plane, we consider the weighted space H-v(infinity) (G)of all holomorphic functions on G such that the product v vertical bar f vertical bar is bounded in G and study the question of when such a space is complete under the canonical sup-seminorm. We obtain both some necessary and some sufficient conditions in terms of the weight v, exhibit several relevant examples, and characterize completeness in the case of spaces with radial weights on balanced domains.The first author was partially supported by MTM2013-43540-P and MTM2016-76647-P by MINECO/FEDER-EU and GVA Prometeo II/2013/013. The second author was partially supported by the MINECO/FEDER-EU Grant MTM2015-65792-P. Both authors were partially supported by Thematic Research Network MTM2015-69323-REDT, MINECO, Spain.Bonet Solves, JA.; Vukotic, D. (2017). A note on completeness of weighted normed spaces of analytic functions. Results in Mathematics. 72(1-2):263-279. https://doi.org/10.1007/s00025-017-0696-2S263279721-2Arcozzi, N., Björn, A.: Dominating sets for analytic and harmonic functions and completeness of weighted Bergman spaces. Math. Proc. R. Ir. Acad. 102A, 175–192 (2002)Berenstein, C.A., Gay, R.: Complex Variables, An Introduction. Springer, New York (1991)Bierstedt, K.D., Bonet, J., Galbis, A.: Weighted spaces of holomorphic functions on bounded domains. Mich. Math. J. 40, 271–297 (1993)Bierstedt, K.D., Bonet, J., Taskinen, J.: Associated weights and spaces of holomorphic functions. Stud. Math. 127, 137–168 (1998)Björn, A.: Removable singularities for weighted Bergman spaces. Czechoslov. Math. J. 56, 179–227 (2006)Bonet, J., Domański, P., Lindström, M.: Essential norm and weak compactness of composition operators on weighted Banach spaces of analytic functions. Can. Math. Bull. 42(2), 139–148 (1999)Bonet, J., Vogt, D.: Weighted spaces of holomorphic functions and sequence spaces. Note Mat. 17, 87–97 (1997)Conway, J.B.: Functions of One Complex Variable, Second Edition, Graduate Texts in Mathematics, vol. 11. Springer, New York (1978)Gaier, D.: Lectures on Complex Approximation. Birkhäuser, Boston (1987)Grosse-Erdmann, K.-G.: A weak criterion for vector-valued holomorphic functions. Math. Proc. Camb. Philos. Soc. 136, 399–411 (2004)Hörmander, L.: An Introduction to Complex Analysis in Several Variables. North-Holland, Amsterdam (1979)Horváth, J.: Topological Vector Spaces and Distributions. Addison-Wesley, Reading (1966)Lusky, W.: On weighted spaces of harmonic and holomorphic functions. J. Lond. Math. Soc. 51, 309–320 (1995)Lusky, W.: On the isomorphism classes of weighted spaces of harmonic and holomorphic functions. Stud. Math. 175, 19–45 (2006)Nakazi, T.: Weighted Bloch spaces which are Banach spaces. Rend. Circ. Mat. Palermo 62, 427–440 (2013)Shields, A.L., Williams, D.L.: Bounded projections, duality and multipliers in spaces of analytic functions. Trans. Am. Math. Soc. 162, 287–302 (1971

Weighted Banach spaces of harmonic functions

“The final publication is available at Springer via http://dx.doi.org/10.1007/s13398-012-0109-z."We study Banach spaces of harmonic functions on open sets of or endowed with weighted supremum norms. We investigate the harmonic associated weight defined naturally as the analogue of the holomorphic associated weight introduced by Bierstedt, Bonet, and Taskinen and we compare them. We study composition operators with holomorphic symbol between weighted Banach spaces of pluriharmonic functions characterizing the continuity, the compactness and the essential norm of composition operators among these spaces in terms of associated weights.The research of the first author was partially supported by MEC and FEDER Project MTM2010-15200 and by GV project ACOMP/2012/090.Jorda Mora, E.; Zarco García, AM. (2014). Weighted Banach spaces of harmonic functions. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas. 108(2):405-418. https://doi.org/10.1007/s13398-012-0109-zS4054181082Axler, S., Bourdon, P., Ramey, W.: Harmonic Function Theory, 2nd edn. Springer, Berlin (2001)Bierstedt, K.D., Bonet, J., Galbis, A.: Weighted spaces of holomorphic functions on balanced domains. Mich. Math. J. 40(2), 271–297 (1993)Bierstedt, K.D., Bonet, J., Taskinen, J.: Associated weights and spaces of holomorphic functions. Stud. Math. 127(2), 137–168 (1998)Bierstedt, K.D., Summers, W.H.: Biduals of weighted Banach spaces of analytic functions. J. Aust. Math. Soc. Ser. A 54(1), 70–79 (1993)Bonet, J., Domański, P., Lindström, M.: Essential norm and weak compactness of composition operators on weighted Banach spaces of analytic functions. Can. Math. Bull. 42(2), 139–148 (1999)Bonet, J., Domański, P., Lindström, M.: Weakly compact composition operators on weighted vector-valued Banach spaces of analytic mappings. Ann. Acad. Sci. Fenn. Math. Ser. A I 26, 233–248 (2001)Bonet, J., Domański, P., Lindström, M., Taskinen, J.: Composition operators between weighted Banach spaces of analytic functions. J. Aust. Math. Soc. Ser. A 64, 101–118 (1998)Bonet, J., Friz, M., Jordá, E.: Composition operators between weighted inductive limits of spaces of holomorphic functions. Publ. Math. Debr. Ser. A 67, 333–348 (2005)Boyd, C., Rueda, P.: The v-boundary of weighted spaces of holomorphic functions. Ann. Acad. Sci. Fenn. Math. 30, 337–352 (2005)Boyd, C., Rueda, P.: Complete weights and v-peak points of spaces of weighted holomorphic functions. Isr. J. Math. 155, 57–80 (2006)Boyd, C., Rueda, P.: Isometries of weighted spaces of harmonic functions. Potential Anal. 29(1), 37–48 (2008)Carando, D., Sevilla-Peris, P.: Spectra of weighted algebras of holomorphic functions. Math. Z. 263, 887–902 (2009)Contreras, M.D., Hernández-Díaz, G.: Weighted composition operators in weighted Banach spaces of analytic functions. J. Aust. Math. Soc. Ser. A 69(1), 41–60 (2000)García, D., Maestre, M., Rueda, P.: Weighted spaces of holomorphic functions on Banach spaces. Stud. Math. 138(1), 1–24 (2000)García, D., Maestre, M., Sevilla-Peris, P.: Composition operators between weighted spaces of holomorphic functions on Banach spaces. Ann. Acad. Sci. Fenn. Math. 29, 81–98 (2004)Gunning, R., Rossi, H.: Analytic Functions of Several Complex Variables. AMS Chelsea Publishing, Providence (2009)Hoffman, K.: Banach Spaces of Analytic Functions. Prentice-Hall, Englewood Cliffs (1962)Krantz, S.G.: Function Theory of Several Complex Variables. AMS, Providence (2001)Lusky, W.: On weighted spaces of harmonic and holomorphic functions. J. Lond. Math. Soc. 51, 309–320 (1995)Lusky, W.: On the isomorphism classes of weighted spaces of harmonic and holomorphic functions. Stud. Math. 175(1), 19–45 (2006)Meise, R., Vogt, D.: Introduction to Functional Analysis. Oxford University Press, Oxford (1997)Montes-Rodríguez, A.: Weight composition operators on weighted Banach spaces of analytic functions. J. Lond. Math. Soc. 61(2), 872–884 (2000)Ng, K.F.: On a theorem of Diximier. Math. Scand. 29, 279–280 (1972)Rudin, W.: Real and Complex Analysis. MacGraw-Hill, NY (1970)Rudin, W.: Functional analysis. In: International series in pure and applied mathematics, 2nd edn. McGraw-Hill, Inc., New York (1991)Shields, A.L., Williams, D.L.: Bounded projections, duality and multipliers in spaces of harmonic functions. J. Reine Angew. Math. 299(300), 256–279 (1978)Shields, A.L., Williams, D.L.: Bounded projections and the growth of harmonic conjugates in the unit disc. Mich. Math. J. 29, 3–25 (1982)Zheng, L.: The essential norms and spectra of composition operators on $$H^\infty$$ . Pac. J. Math. 203(2), 503–510 (2002

Weighted composition operators on Korenblum type spaces of analytic functions

[EN] We investigate the continuity, compactness and invertibility of weighted composition operators W-psi,W-phi: f -> psi(f circle phi) when they act on the classical Korenblum space A(-infinity) and other related Frechet or (LB)-spaces of analytic functions on the open unit disc which are defined as intersections or unions of weighted Banach spaces with sup-norms. Some results about the spectrum of these operators are presented in case the self-map phi has a fixed point in the unit disc. A precise description of the spectrum is obtained in this case when the operator acts on the Korenblum space.This research was partially supported by the research project MTM2016-76647-P and the grant BES-2017-081200.Gomez-Orts, E. (2020). Weighted composition operators on Korenblum type spaces of analytic functions. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 114(4):1-15. https://doi.org/10.1007/s13398-020-00924-1S1151144Abramovich, Y.A., Aliprantis, C.D.: An invitation to operator theory. Graduate Studies in Mathematics. Amer. Math. Soc., 50 (2002)Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator in the Fréchet spaces $$\ell ^{p+}$$ and $$L^{p-}$$. Glasgow Math. J. 59, 273–287 (2017)Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator on Korenblum type spaces of analytic functions. Collect. Math. 69(2), 263–281 (2018)Albanese, A.A., Bonet, J., Ricker, W.J.: Operators on the Fréchet sequence spaces $$ces(p+), 1\le p\le \infty$$. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113(2), 1533–1556 (2019)Albanese, A.A., Bonet, J., Ricker, W.J.: Linear operators on the (LB)-sequence spaces $$ces(p-), 1\le p\le \infty$$. Descriptive topology and functional analysis. II, 43–67, Springer Proc. Math. Stat., 286, Springer, Cham (2019)Arendt, W., Chalendar, I., Kumar, M., Srivastava, S.: Powers of composition operators: asymptotic behaviour on Bergman, Dirichlet and Bloch spaces. J. Austral. Math. Soc. 1–32. https://doi.org/10.1017/S1446788719000235Aron, R., Lindström, M.: Spectra of weighted composition operators on weighted Banach spaces of analytic funcions. Israel J. Math. 141, 263–276 (2004)Bierstedt, K.D., Summers, W.H.: Biduals of weighted Banach spaces of analytic functions. J. Austral. Math. Soc., Ser. A, 54(1), 70–79 (1993)Bonet, J.: A note about the spectrum of composition operators induced by a rotation. RACSAM 114, 63 (2020). https://doi.org/10.1007/s13398-020-00788-5Bonet, J., Domański, P., Lindström, M., Taskinen, J.: Composition operators between weighted Banach spaces of analytic functions. J. Austral. Math. Soc., Ser. A, 64(1), 101–118 (1998)Bourdon, P.S.: Essential angular derivatives and maximum growth of Königs eigenfunctions. J. Func. Anal. 160, 561–580 (1998)Bourdon, P.S.: Invertible weighted composition operators. Proc. Am. Math. Soc. 142(1), 289–299 (2014)Carleson, L., Gamelin, T.: Complex Dynamics. Springer, Berlin (1991)Cowen, C., MacCluer, B.: Composition Operators on Spaces of Analytic Functions. CRC Press, Boca Raton, FL (1995)Contreras, M., Hernández-Díaz, A.G.: Weighted composition operators in weighted Banach spacs of analytic functions. J. Austral. Math. Soc., Ser. A 69, 41–60 (2000)Eklund, T., Galindo, P., Lindström, M.: Königs eigenfunction for composition operators on Bloch and $$H^\infty$$ spaces. J. Math. Anal. Appl. 445, 1300–1309 (2017)Hedenmalm, H., Korenblum, B., Zhu, K.: Theory of Bergman Spaces. Grad. Texts in Math. 199. Springer, New York (2000)Jarchow, H.: Locally Convex Spaces. Teubner, Stuttgart (1981)Kamowitz, H.: Compact operators of the form $$uC_{\varphi }$$. Pac. J. Math. 80(1) (1979)Korenblum, B.: An extension of the Nevanlinna theory. Acta Math. 135, 187–219 (1975)Köthe, G.: Topological Vector Spaces II. Springer, New York Inc (1979)Lusky, W.: On the isomorphism classes of weighted spaces of harmonic and holomophic functions. Stud. Math. 75, 19–45 (2006)Meise, R., Vogt, D.: Introduction to functional analysis. Oxford Grad. Texts in Math. 2, New York, (1997)Montes-Rodríguez, A.: Weighted composition operators on weighted Banach spaces of analytic functions. J. Lond. Math. Soc. 61(3), 872–884 (2000)Queffélec, H., Queffélec, M.: Diophantine Approximation and Dirichlet series. Hindustain Book Agency, New Delhi (2013)Shapiro, J.H.: Composition Operators and Classical Function Theory. Springer, New York (1993)Shields, A.L., Williams, D.L.: Bounded projections, duality and multipliers in spaces of analytic functions. Trans. Amer. Math. Soc. 162, 287–302 (1971)Zhu, K.: Operator Theory on Function Spaces, Math. Surveys and Monographs, Amer. Math. Soc. 138 (2007

Classical operators on the Hörmander algebras

We study the integration operator, the differentiation operator and more general differential operators on radial Fr´echet or (LB) H¨ormander algebras of entire functions. We analyze when these operators are power bounded, hypercyclic and (uniformly) mean ergodic.This research was partially supported by MEC and FEDER Project MTM2010-15200. The research of M. J. Beltran was also supported by grant F.P.U. AP2008-00604 and Programa de Apoyo a la Investigacion y Desarrollo de la UPV PAID-06-12, and the research of J. Bonet and C. Fernandez, by GVA under Project PROMETEOII/2013/013.Beltrán Meneu, MJ.; Bonet Solves, JA.; Fernández, C. (2015). Classical operators on the Hörmander algebras. Discrete and Continuous Dynamical Systems - Series A. 35(2):637-652. https://doi.org/10.3934/dcds.2015.35.637S63765235

High body mass index is not associated with atopy in schoolchildren living in rural and urban areas of Ghana

<p>Abstract</p> <p>Background</p> <p>Factors which determine the development of atopy and the observed rural-urban gradient in its prevalence are not fully understood. High body mass index (BMI) has been associated with asthma and potentially atopy in industrialized countries. In developing countries, the transition from rural to urban areas has been associated with lifestyle changes and an increased prevalence of high BMI; however, the effect of high BMI on atopy remains unknown in this population. We therefore investigated the association between high BMI and atopy among schoolchildren living in rural and urban areas of Ghana.</p> <p>Methods</p> <p>Data on skin prick testing, anthropometric, parasitological, demographic and lifestyle information for 1,482 schoolchildren aged 6-15 years was collected. Atopy was defined as sensitization to at least one tested allergen whilst the Centres for Disease Control and Prevention (CDC, Atlanta) growth reference charts were used in defining high BMI as BMI ≥ the 85^thpercentile. Logistic regression was performed to investigate the association between high BMI and atopy whilst adjusting for potential confounding factors.</p> <p>Results</p> <p>The following prevalences were observed for high BMI [Rural: 16%, Urban: 10.8%, p < 0.001] and atopy [Rural: 25.1%, Urban: 17.8%, p < 0.001]. High BMI was not associated with atopy; but an inverse association was observed between underweight and atopy [OR: 0.57, 95% CI: 0.33-0.99]. Significant associations were also observed with male sex [Rural: OR: 1.49, 95% CI: 1.06-2.08; Urban: OR: 1.90, 95% CI: 1.30-2.79], and in the urban site with older age [OR: 1.76, 95% CI: 1.00-3.07], family history of asthma [OR: 1.58, 95% CI: 1.01-2.47] and occupational status of parent [OR: 0.33, 95% CI: 0.12-0.93]; whilst co-infection with intestinal parasites [OR: 2.47, 95% CI: 1.01-6.04] was associated with atopy in the rural site. After multivariate adjustment, male sex, older age and family history of asthma remained significant.</p> <p>Conclusions</p> <p>In Ghanaian schoolchildren, high BMI was not associated with atopy. Further studies are warranted to clarify the relationship between body weight and atopy in children subjected to rapid life-style changes associated with urbanization of their environments.</p

Quantification of Optic Disc Edema during Exposure to High Altitude Shows No Correlation to Acute Mountain Sickness

BACKGROUND: The study aimed to quantify changes of the optic nerve head (ONH) during exposure to high altitude and to assess a correlation with acute mountain sickness (AMS). This work is related to the Tuebingen High Altitude Ophthalmology (THAO) study. METHODOLOGY/PRINCIPAL FINDINGS: A confocal scanning laser ophthalmoscope (cSLO, Heidelberg Retina Tomograph, HRT3®) was used to quantify changes at the ONH in 18 healthy participants before, during and after rapid ascent to high altitude (4559 m). Slitlamp biomicroscopy was used for clinical optic disc evaluation; AMS was assessed with Lake Louise (LL) and AMS-cerebral (AMS-c) scores; oxygen saturation (SpO₂) and heart rate (HR) were monitored. These parameters were used to correlate with changes at the ONH. After the first night spent at high altitude, incidence of AMS was 55% and presence of clinical optic disc edema (ODE) 79%. Key stereometric parameters of the HRT3® used to describe ODE (mean retinal nerve fiber layer [RNFL] thickness, RNFL cross sectional area, optic disc rim volume and maximum contour elevation) changed significantly at high altitude compared to baseline (p&lt;0.05) and were consistent with clinically described ODE. All changes were reversible in all participants after descent. There was no significant correlation between parameters of ODE and AMS, SpO₂ or HR. CONCLUSIONS/SIGNIFICANCE: Exposure to high altitude leads to reversible ODE in the majority of healthy subjects. However, these changes did not correlate with AMS or basic physiologic parameters such as SpO₂ and HR. For the first time, a quantitative approach has been used to assess these changes during acute, non-acclimatized high altitude exposure. In conclusion, ODE presents a reaction of the body to high altitude exposure unrelated to AMS

A CI-Independent Form of Replicative Inhibition: Turn Off of Early Replication of Bacteriophage Lambda

Several earlier studies have described an unusual exclusion phenotype exhibited by cells with plasmids carrying a portion of the replication region of phage lambda. Cells exhibiting this inhibition phenotype (IP) prevent the plating of homo-immune and hybrid hetero-immune lambdoid phages. We have attempted to define aspects of IP, and show that it is directed to repλ phages. IP was observed in cells with plasmids containing a λ DNA fragment including oop, encoding a short OOP micro RNA, and part of the lambda origin of replication, oriλ, defined by iteron sequences ITN1-4 and an adjacent high AT-rich sequence. Transcription of the intact oop sequence from its promoter, pO is required for IP, as are iterons ITN3–4, but not the high AT-rich portion of oriλ. The results suggest that IP silencing is directed to theta mode replication initiation from an infecting repλ genome, or an induced repλ prophage. Phage mutations suppressing IP, i.e., Sip, map within, or adjacent to cro or in O, or both. Our results for plasmid based IP suggest the hypothesis that there is a natural mechanism for silencing early theta-mode replication initiation, i.e. the buildup of λ genomes with oop+ oriλ+ sequence

Repression of bovine papilloma virus replication is mediated by a virally encoded trans-acting factor

Cells transformed with bovine papilloma virus type 1 mutants in the E6 or E6/7 genes are resistant to high-copy-number amplification of wild-type DNA after supertransfection. Transient and stable replication assays demonstrate this effect. If the supertransfected DNA has a mutation in a newly defined gene (M), this cellular immunity to high-copy-number replication is overcome, resulting in transient replication of the input DNA. In contrast, the resident plasmid does not participate in amplification and is maintained at a constant low copy number. Cotransformation of M- mutants and wild-type DNA into these cells leads to shutoff of replication of both genomes. Thus, M- mutants define a trans-acting negative modulator that regulates viral replication. This function is distinct from the positive factors required for replication. We propose a model that explains why the loss of E6 and E6/7 function leads to immunity of the infected cell