Characterizing Fréchet-Schwartz spaces via power bounded operators

[EN] We characterize Köthe echelon spaces (and, more generally, those Fréchet spaces with an unconditional basis) which are Schwartz, in terms of the convergence of the Cesàro means of power bounded operators defined on them. This complements similar known characterizations of reflexive and of Fréchet–Montel spaces with a basis. Every strongly convergent sequence of continuous linear operators on a FréchetSchwartz space does so in a special way. We single out this type of “rapid convergence” for a sequence of operators and study its relationship to the structure of the underlying space. Its relevance for Schauder decompositions and the connection to mean ergodic operators on Fréchet–Schwartz spaces is also investigated.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. (2014). Characterizing Fréchet-Schwartz spaces via power bounded operators. Studia Mathematica. 224(1):25-45. https://doi.org/10.4064/sm224-1-22545224

CCBE1 in Cardiac Development and Disease

Funding Information: Funding: OB was a pre-doctoral fellow of Fundação para a Ciência e Tecnologia (PD/BD/105891/2015). This work was supported by Fundação para a Ciência e a Tecnologia (FCT) grants (PTDC/SAU-ENB/121095/2010, HMSP-ICT/0039/2013 and 02/SAICT/2017/029590) to JA Belo and by the Scientific Employment Stimulus to JMI (Norma Transitória 8189/2018, FCT), and iNOVA4Health – UIDB/Multi/04462/2020 and UIDP/Multi/04462/2020, a program financially supported by Fundação para a Ciência e Tecnologia / Ministério da Educação e Ciência, through national funds is acknowledged.The collagen- and calcium-binding EGF-like domains 1 (CCBE1) is a secreted protein extensively described as indispensable for lymphangiogenesis during development enhancing VEGF-C signaling. In human patients, mutations in CCBE1 have been found to cause Hennekam syndrome, an inherited disease characterized by malformation of the lymphatic system that presents a wide variety of symptoms such as primary lymphedema, lymphangiectasia, and heart defects. Importantly, over the last decade, an essential role for CCBE1 during heart development is being uncovered. In mice, Ccbe1 expression was initially detected in distinct cardiac progenitors such as first and second heart field, and the proepicardium. More recently, Ccbe1 expression was identified in the epicardium and sinus venosus (SV) myocardium at E11.5–E13.5, the stage when SV endocardium–derived (VEGF-C dependent) coronary vessels start to form. Concordantly, CCBE1 is required for the correct formation of the coronary vessels and the coronary artery stem in the mouse. Additionally, Ccbe1 was found to be enriched in mouse embryonic stem cells (ESC) and revealed as a new essential gene for the differentiation of ESC-derived early cardiac precursor cell lineages. Here, we bring an up-to-date review on the role of CCBE1 in cardiac development, function, and human disease implications. Finally, we envisage the potential of this molecule’s functions from a regenerative medicine perspective, particularly novel therapeutic strategies for heart disease.publishersversionpublishe

The history of a quiet-Sun magnetic element revealed by IMaX/SUNRISE

Isolated flux tubes are considered to be fundamental magnetic building blocks of the solar photosphere. Their formation is usually attributed to the concentration of magnetic field to kG strengths by the convective collapse mechanism. However, the small size of the magnetic elements in quiet-Sun areas has prevented this scenario from being studied in fully resolved structures. Here we report on the formation and subsequent evolution of one such photospheric magnetic flux tube, observed in the quiet Sun with unprecedented spatial resolution (0\farcs 15 - 0\farcs 18) and high temporal cadence (33 s). The observations were acquired by the Imaging Magnetograph Experiment (IMaX) aboard the \textsc{Sunrise} balloon-borne solar observatory. The equipartition field strength magnetic element is the result of the merging of several same polarity magnetic flux patches, including a footpoint of a previously emerged loop. The magnetic structure is then further intensified to kG field strengths by convective collapse. The fine structure found within the flux concentration reveals that the scenario is more complex than can be described by a thin flux tube model with bright points and downflow plumes being established near the edges of the kG magnetic feature. We also observe a daisy-like alignment of surrounding granules and a long-lived inflow towards the magnetic feature. After a subsequent weakening process, the field is again intensified to kG strengths. The area of the magnetic feature is seen to change in anti-phase with the field strength, while the brightness of the bright points and the speed of the downflows varies in phase. We also find a relation between the brightness of the bright point and the presence of upflows within it.Comment: 13 pages. Accepted in ApJ. Animation 1 can be viewed and downloaded from: http://spg.iaa.es/downloads.as

Norm-attaining weighted composition operators on weighted Banach spaces of analytic functions

The final publication is available at Springer via http://dx.doi.org/10.1007/s00013-012-0458-zWe investigate weighted composition operators that attain their norm on weighted Banach spaces of holomorphic functions on the unit disc of type H∞. Applications for composition operators on weighted Bloch spaces are given. © 2012 Springer Basel.1. The authors are thankful to the referee for pointing to us the references [15] and [16] and their relevance in the present research. 2. The research of Bonet was partially supported by MICINN and FEDER Project MTM2010-15200 and by GV project Prometeo/2008/101 and project ACOMP/2012/090.Bonet Solves, JA.; Lindström, M.; Wolf, E. (2012). Norm-attaining weighted composition operators on weighted Banach spaces of analytic functions. Archiv der Mathematik. 99(6):537-546. https://doi.org/10.1007/s00013-012-0458-zS537546996Bierstedt K.D., Bonet J., Galbis A.: Weighted spaces of holomorphic functions on bounded domains. Michigan Math. J. 40, 271–297 (1993)Bierstedt K.D., Bonet J., Taskinen J.: Associated weights and spaces of holomorphic functions. Studia Math. 127, 137–168 (1998)J. Bonet, P. Domański, and M. Lindström, Essential norm and weak compactness of composition operators on weighted Banach spaces of analytic functions. Canad, Math. Bull. 42, no. 2, (1999), 139–148Bonet J. et al.: Composition operators between weighted Banach spaces of analytic functions. J. Austral. Math. Soc. Ser. A 64, 101–118 (1998)Bonet J., Lindström M, Wolf E.: Isometric weighted composition operators on weighted Banach spaces of type H ∞. Proc. Amer. Math. Soc. 136, 4267–4273 (2008)Bonet J, Wolf E.: A note on weighted spaces of holomorphic functions. Archiv Math. 81, 650–654 (2003)Contreras M.D, Hernández-Díaz A.G.: Weighted composition operators in weighted banach spaces of analytic functions. J. Austral. Math. Soc. Ser. A 69, 41–60 (2000)Cowen C., MacCluer B.: Composition Operators on Spaces of Analytic Functions. CRC Press, Boca Raton (1995)J. Diestel, Geometry of Banach Spaces. Selected Topics, Lecture Notes in Math. vol. 485, Springer, Berlin, 1975.Hammond C.: On the norm of a composition operator with linear fractional symbol. Acta Sci. Math. (Szeged) 69, 813–829 (2003)Hosokawa T., Izuchi K., Zheng D.: Isolated points and essential components of composition operators on H ∞. Proc. Amer. Math. Soc. 130, 1765–1773 (2001)Hosokava T., Ohno S.: Topological strusctures of the sets of composition operatorson the Bloch spaces. J. Math. anal. Appl. 303, 499–508 (2005)Lusky W.: On the isomorphy classes of weighted spaces of harmonic and holomorphic functions. Studia Math. 175, 19–45 (2006)Martín M.: Norm-attaining composition operators on the Bloch spaces. J. Math. Anal. Appl. 369, 15–21 (2010)A. Montes-Rodríguez, The Pick-Schwarz lemma and composition operators on Bloch spaces, International Workshop on Operator Theory (Cefalu, 1997), Rend. Circ. Mat. Palermo (2) Suppl. 56 (1998), 167–170.Montes-Rodríguez A.: The essential norm of a composition operator on Bloch spaces. Pacific J. Math. 188, 339–351 (1999)Montes-Rodríguez A.: Weighted composition operators on weighted Banach spaces of analytic functions. J. London Math. Soc. 61, 872–884 (2000)J.H. Shapiro, Composition Operators and Classical Function Theory, Springer, 1993.K. Zhu, Operator Theory in Function Spaces, Second Edition. Amer. Math. Soc., 2007

Inelastic Effective Length Factor of Nonsway Reinforced Concrete Columns

[EN] This paper proposes a new equation for the effective length factor k-factor for reinforced concrete columns in braced frames. The new formula is valid both for normal and high-strength concrete. The equation was obtained from a sensitivity analysis performed on a two-dimensional nonlinear finite-element numerical model that takes into account the inelastic behavior of the concrete columns cracking, yielding, and second order effects. The numerical model was calibrated with 44 experimental tests performed by the writers¿ research group. A comparative study was carried out between the numerical model and different national design codes, displaying important differences with respect to all of them: the ACI code from 37 to 3%, the Spanish code EHE from 26 to 9.26%, and the Eurocode 2 from 14 to 14%. It was decided to propose two additional simplified equations: one for checking and the second for design.The authors wish to express their sincere gratitude to the Spanish Ministerio de Fomento for help provided through project 13-12-2001 and Ministerio de Educación through BIA2005-255.Bendito, A.; Romero, ML.; Bonet Senach, JL.; Miguel Sosa, P.; Fernández Prada, MÁ. (2009). Inelastic Effective Length Factor of Nonsway Reinforced Concrete Columns. Journal of Structural Engineering. 135(9):1034-1039. https://doi.org/10.1061/(ASCE)0733-9445(2009)135:9(1034)S10341039135

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

Spectrum and compactness of the Cesàro operator on weighted l_p spaces

[EN] An investigation is made of the continuity, the compactness and the spectrum of the Ces`aro operator C when acting on the weighted Banach sequence spaces l_p(w), 1 < p < 1, for a positive decreasing weight w, thereby extending known results for C when acting on the classical spaces l_p. New features arise in the weighted setting (for example, existence of eigenvalues, compactness) which are not present in l_p.The research of the first two authors was partially supported by the projects MTM2013-43540-P and GVA Prometeo II/2013/013 (Spain).Albanese, A.; Bonet Solves, JA.; Ricker, WJ. (2015). Spectrum and compactness of the Cesàro operator on weighted l_p spaces. Journal of the Australian Mathematical Society. 99(3):287-314. https://doi.org/10.1017/S1446788715000221S28731499