340 research outputs found
Continuity of homomorphisms and derivations from algebras of approximable and nuclear operators
1. Let be a Banach algebra. We say that homomorphisms from are continuous if every homomorphism from into a Banach algebra is automatically continuous, and that derivations from are continuous if every derivation from into a Banach -bimodule is automatically continuou
Self-induced compactness in Banach spaces
We consider the question: is every compact set in a Banach space X contained in the closed unit range of a compact (or even approximable) operator on X? We give large classes of spaces where the question has an affirmative answer, but observe that it has a negative answer, in general, for approximable operators. We further construct a Banach space failing the bounded compact approximation property, though all of its duals have the metric compact approximation propert
DUALITY FOR SOME LARGE SPACES OF ANALYTIC FUNCTIONS
We characterize the duals and biduals of the -analogues of the standard Nevanlinna classes , and . We adopt the convention to take to be the classical Smirnov class for , and the Hardy-Orlicz space for . Our results generalize and unify earlier characterizations obtained by Eoff for and , and by Yanigahara for the Smirnov class. Each is a complete metrizable topological vector space (in fact, even an algebra); it fails to be locally bounded and locally convex but admits a separating dual. Its bidual will be identified with a specific nuclear power series space of finite type; this turns out to be the ‘Fréchet envelope' of as well. The generating sequence of this power series space is of the form for some . For example, the s in the interval (\smfr12,1) correspond in a bijective fashion to the Nevanlinna classes , , whereas the s in the interval (0,\smfr12) correspond bijectively to the Hardy-Orlicz spaces , . By the work of Yanagihara, \theta=\smfr12 corresponds to . As in the work by Yanagihara, we derive our results from characterizations of coefficient multipliers from into various smaller classical spaces of analytic functions on . AMS 2000 Mathematics subject classification: Primary 46E10; 46A11; 47B38. Secondary 30D55; 46A45; 46E15\vskip-3p
Response of Ambulatory Human Subjects to Artificial Gravity (Short Radius Centrifugation)
Prolonged exposure to microgravity results in significant adaptive changes, including cardiovascular deconditioning, muscle atrophy, bone loss, and sensorimotor reorganization, that place individuals at risk for performing physical activities after return to a gravitational environment. Planned missions to Mars include unprecedented hypogravity exposures that would likely result in unacceptable risks to crews. Artificial gravity (AG) paradigms may offer multisystem protection from the untoward effects of adaptation to the microgravity of space or the hypogravity of planetary surfaces. While the most effective AG designs would employ a rotating spacecraft, perceived issues may preclude their use. The questions of whether and how intermittent AG produced by a short radius centrifuge (SRC) could be employed have therefore sprung to the forefront of operational research. In preparing for a series of intermittent AG trials in subjects deconditioned by bed rest, we have examined the responses of several healthy, ambulatory subjects to SRC exposures
Searches for HCl and HF in comets 103P/Hartley 2 and C/2009 P1 (Garradd) with the Herschel space observatory
HCl and HF are expected to be the main reservoirs of fluorine and chlorine
wherever hydrogen is predominantly molecular. They are found to be strongly
depleted in dense molecular clouds, suggesting freeze-out onto grains in such
cold environments. We can then expect that HCl and HF were also the major
carriers of Cl and F in the gas and icy phases of the outer solar nebula, and
were incorporated into comets. We aimed to measure the HCl and HF abundances in
cometary ices as they can provide insights on the halogen chemistry in the
early solar nebula. We searched for the J(1-0) lines of HCl and HF at 626 and
1232 GHz, respectively, using the HIFI instrument on board the Herschel Space
Observatory. HCl was searched for in comets 103P/Hartley 2 and C/2009 P1
(Garradd), whereas observations of HF were conducted in comet C/2009 P1. In
addition, observations of HO and HO lines were performed in C/2009
P1 to measure the HO production rate. Three lines of CHOH were
serendipitously observed in the HCl receiver setting. HCl is not detected,
whereas a marginal (3.6-) detection of HF is obtained. The upper limits
for the HCl abundance relative to water are 0.011% and 0.022%, for 103P and
C/2009 P1, respectively, showing that HCl is depleted with respect to the solar
Cl/O abundance by a factor more than 6 in 103P, where the error is
related to the uncertainty in the chlorine solar abundance. The marginal HF
detection obtained in C/2009 P1 corresponds to an HF abundance relative to
water of (1.80.5) 10, which is approximately consistent
with a solar photospheric F/O abundance. The observed depletion of HCl suggests
that HCl was not the main reservoir of chlorine in the regions of the solar
nebula where these comets formed. HF was possibly the main fluorine compound in
the gas phase of the outer solar nebula.Comment: Accepted for publication in Astronomy & Astrophysic
Controllability on infinite-dimensional manifolds
Following the unified approach of A. Kriegl and P.W. Michor (1997) for a
treatment of global analysis on a class of locally convex spaces known as
convenient, we give a generalization of Rashevsky-Chow's theorem for control
systems in regular connected manifolds modelled on convenient
(infinite-dimensional) locally convex spaces which are not necessarily
normable.Comment: 19 pages, 1 figur
Factorization of strongly (p,sigma)-continuous multilinear operators
We introduce the new ideal of strongly-continuous linear operators in order to study the adjoints of the -absolutely continuous linear operators. Starting from this ideal we build a new multi-ideal by using the composition method. We prove the corresponding Pietsch domination theorem and we present a representation of this multi-ideal by a tensor norm. A factorization theorem characterizing the corresponding multi-ideal - which is also new for the linear case - is given. When applied to the case of the Cohen strongly -summing operators, this result gives also a new factorization theorem.D. Achour acknowledges with thanks the support of the Ministere de l'Enseignament Superieur et de la Recherche Scientifique (Algeria) under project PNR 8-U28-181. E. Dahia acknowledges with thanks the support of the Ministere de l'Enseignament Superieur et de la Recherche Scientifique (Algeria) [grant number 10/PG-FMI/2013] and the Universite de M'Sila (2013) for short term stage. P. Rueda acknowledges with thanks the support of the Ministerio de Economia y Competitividad (Spain) MTM2011-22417. E. A. Sanchez Perez acknowledges with thanks the support of the Ministerio de Economia y Competitividad (Spain) under project MTM2012-36740-C02-02.Achour, D.; Dahia, E.; Rueda, P.; Sánchez Pérez, EA. (2014). Factorization of strongly (p,sigma)-continuous multilinear operators. Linear and Multilinear Algebra. 62(12):1649-1670. doi:10.1080/03081087.2013.839677S164916706212Matter, U. (1987). Absolutely Continuous Operators and Super-Reflexivity. Mathematische Nachrichten, 130(1), 193-216. doi:10.1002/mana.19871300118Diestel, J., Jarchow, H., & Tonge, A. (1995). Absolutely Summing Operators. doi:10.1017/cbo9780511526138Pietsch, A. (1967). Absolut p-summierende Abbildungen in normierten Räumen. Studia Mathematica, 28(3), 333-353. doi:10.4064/sm-28-3-333-353Achour, D., & Mezrag, L. (2007). On the Cohen strongly p-summing multilinear operators. Journal of Mathematical Analysis and Applications, 327(1), 550-563. doi:10.1016/j.jmaa.2006.04.065Apiola, H. (1976). Duality between spaces ofp-summable sequences, (p, q)-summing operators and characterizations of nuclearity. Mathematische Annalen, 219(1), 53-64. doi:10.1007/bf01360858Sánchez PérezEA. Ideales de operadores absolutamente continuos y normas tensoriales asociadas [PhD Thesis]. Spain: Universidad Politécnica de Valencia; 1997.López Molina, J. A., & Sánchez Pérez, E. A. (2000). On operator ideals related to (p,σ)-absolutely continuous operators. Studia Mathematica, 138(1), 25-40. doi:10.4064/sm-138-1-25-40Cohen, J. S. (1973). Absolutelyp-summing,p-nuclear operators and their conjugates. Mathematische Annalen, 201(3), 177-200. doi:10.1007/bf01427941Mezrag, L., & Saadi, K. (2012). Inclusion and coincidence properties for Cohen strongly summing multilinear operators. Collectanea Mathematica, 64(3), 395-408. doi:10.1007/s13348-012-0071-2Achour, D., & Alouani, A. (2010). On multilinear generalizations of the concept of nuclear operators. Colloquium Mathematicum, 120(1), 85-102. doi:10.4064/cm120-1-7Mujica, X. (2008). τ(p;q)-summing mappings and the domination theorem. Portugaliae Mathematica, 211-226. doi:10.4171/pm/1806Campos, J. R. (2013). Cohen and multiple Cohen strongly summing multilinear operators. Linear and Multilinear Algebra, 62(3), 322-346. doi:10.1080/03081087.2013.779270Bu, Q., & Shi, Z. (2013). On Cohen almost summing multilinear operators. Journal of Mathematical Analysis and Applications, 401(1), 174-181. doi:10.1016/j.jmaa.2012.12.005Ryan, R. A. (2002). Introduction to Tensor Products of Banach Spaces. Springer Monographs in Mathematics. doi:10.1007/978-1-4471-3903-4Achour, D., & Belaib, M. T. (2011). Tensor norms related to the space of Cohen -nuclear‎ ‎multilinear mappings. Annals of Functional Analysis, 2(1), 128-138. doi:10.15352/afa/1399900268Achour, D. (2011). Multilinear extensions of absolutely (p;q;r)-summing operators. Rendiconti del Circolo Matematico di Palermo, 60(3), 337-350. doi:10.1007/s12215-011-0054-2Dahia, E., Achour, D., & Sánchez Pérez, E. A. (2013). Absolutely continuous multilinear operators. Journal of Mathematical Analysis and Applications, 397(1), 205-224. doi:10.1016/j.jmaa.2012.07.034Botelho, G., Pellegrino, D., & Rueda, P. (2007). On Composition Ideals of Multilinear Mappings and Homogeneous Polynomials. Publications of the Research Institute for Mathematical Sciences, 43(4), 1139-1155. doi:10.2977/prims/1201012383Pellegrino, D., Santos, J., & Seoane-Sepúlveda, J. B. (2012). Some techniques on nonlinear analysis and applications. Advances in Mathematics, 229(2), 1235-1265. doi:10.1016/j.aim.2011.09.014Ramanujan, M. S., & Schock, E. (1985). Operator ideals and spaces of bilinear operators. Linear and Multilinear Algebra, 18(4), 307-318. doi:10.1080/03081088508817695Floret, K., & Hunfeld, S. (2002). Proceedings of the American Mathematical Society, 130(05), 1425-1436. doi:10.1090/s0002-9939-01-06228-
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 FÃsicas 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 Cesà ro operator in the Fréchet spaces and . Glasgow Math. J. 59, 273–287 (2017)Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesà ro 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 . Rev. R. Acad. Cienc. Exactas FÃs. 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 . 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., DomaÅ„ski, 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-DÃaz, 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 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 . 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-RodrÃguez, 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
Dynamics and spectrum of the Cesà ro operator on C-infinity(R+)
[EN] The spectrum and point spectrum of the Cesaro averaging operator C acting on the Frechet space C-infinity(R+) of all C-infinity functions on the interval [0, infinity) are determined. We employ an approach via C-0-semigroup theory for linear operators. A spectral mapping theorem for the resolvent of a closed operator acting on a locally convex space is established; it constitutes a useful tool needed to establish the main result. The dynamical behaviour of C is also investigated.The research of the first two authors was partially supported by the projects MTM2013-43540-P, GVA Prometeo II/2013/013 and GVA ACOMP/2015/186 (Spain).Albanese, AA.; Bonet Solves, JA.; Ricker, WJ. (2016). Dynamics and spectrum of the Cesà ro operator on C-infinity(R+). Monatshefte für Mathematik. 181:267-283. https://doi.org/10.1007/s00605-015-0863-zS267283181Albanese, 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.: Mean ergodic semigroups of operators. Rev. R. Acad. Cien. Serie A Mat. RACSAM 106, 299–319 (2012)Albanese, A.A., Bonet, J., Ricker, W.J.: Montel resolvents and uniformly mean ergodic semigroups of linear operators. Quaest. Math. 36, 253–290 (2013)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.: Uniform mean ergodicity of C 0 -semigroups in a class of in Fréchet spaces. Funct. Approx. Comment. Math. 50, 307–349 (2014)Albanese, A.A., Bonet, J., Ricker, W.J.: On the continuous Cesà ro operator in certain function spaces. Positivity 19, 659–679 (2015)Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesà ro operator in the Fréchet spaces ℓ p + and L p - . Glasgow Math. J. (accepted)Arendt, W.: Gaussian estimates and interpolation of the spectrum in L p . Diff. Int. Equ. 7, 1153–1168 (1994)Bayart, F., Matheron, E.: Dynamics of linear operators. Cambridge Tracts in Mathematics, vol. 179. Cambridge University Press, Cambridge (2009)Boyd, D.W.: The spectrum of the Cesà ro operator. Acta Sci. Math. (Szeged) 29, 31–34 (1968)Grosse-Erdmann, K.G., Manguillot, A.P.: Linear chaos. Universitext, Springer Verlag, London (2011)Hille, E.: Remarks on ergodic theorems. Trans. Am. Math. Soc. 57, 246–269 (1945)Jarchow, H.: Locally convex spaces. Teubner, Stuttgart (1981)Komura, T.: Semigroups of operators in locally convex spaces. J. Funct. Anal. 2, 258–296 (1968)Lin, M.: On the uniform ergodic theorem. Proc. Am. Math. Soc. 43, 337–340 (1974)Malgrange, B.: Idéaux de fonctions différentiables et division des distributions. Distributions, Editions École Polytechnique, Palaiseau, pp. 1–21 (2003)Meise, R., Vogt, D.: Introduction to functional analysis. Oxford Graduate Texts in Mathematics, vol. 2. The Clarendon Press. Oxford University Press, New York (1997)Seeley, R.T.: Extension of C ∞ functions defined in a half space. Proc. Am. Math. Soc. 15, 625–626 (1964)Siskakis, A.G.: Composition semigroups and the Cesà ro operator. J. London Math. Soc. (2) 36, 153–164 (1987)Yosida, K.: Functional analysis. Springer, New York, Berlin, Heidelberg (1980)Valdivia, M.: Topics in locally convex spaces. North-Holland Math. Stud. 67, North-Holland, Amsterdam (1982
Operators on the Fréchet sequence space ces(p+),
[EN] The Fréchet sequence spaces ces(p+) are very different to the Fréchet sequence spaces ¿p+,1¿pp}\ell ^q ℓ p + = ∩ q > p ℓ q . Math. Nachr. 147, 7–12 (1990)Pérez Carreras, P., Bonet, J.: Barrelled Locally Convex Spaces. North Holland, Amsterdam (1987)Pitt, H.R.: A note on bilinear forms. J. Lond. Math. Soc. 11, 171–174 (1936)Ricker, W.J.: A spectral mapping theorem for scalar-type spectral operators in locally convex spaces. Integral Equ. Oper. Theory 8, 276–288 (1985)Robertson, A.P., Robertson, W.: Topological Vector Spaces. Cambridge University Press, Cambridge (1973)Waelbroeck, L.: Topological vector spaces and algebras. Lecture Notes in Mathematics, vol. 230. Springer, Berlin (1971
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