Artículo

Muro, S.; Pinasco, D.; Savransky, M. "Dynamics of non-convolution operators and holomorphy types" (2018) Journal of Mathematical Analysis and Applications. 468(2):622-641
El editor solo permite decargar el artículo en su versión post-print desde el repositorio. Por favor, si usted posee dicha versión, enviela a
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

In this article we study the hypercyclic behavior of non-convolution operators defined on spaces of analytic functions of different holomorphy types over Banach spaces. The operators in the family we analyze are a composition of differentiation and composition operators, and are extensions of operators in H(C) studied by Aron and Markose in 2004. The dynamics of this class of operators, in the context of one and several complex variables, was further investigated by many authors. It turns out that the situation is somewhat different and that some purely infinite dimensional difficulties appear. For example, in contrast to the several complex variable case, it may happen that the symbol of the composition operator has no fixed points and still, the operator is not hypercyclic. We also prove a Runge type theorem for holomorphy types on Banach spaces. © 2018 Elsevier Inc.

Registro:

Documento: Artículo
Título:Dynamics of non-convolution operators and holomorphy types
Autor:Muro, S.; Pinasco, D.; Savransky, M.
Filiación:Departamento de Matemática – Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, Ciudad Autónoma de Buenos Aires, 1428, Argentina
CIFASIS-CONICET, Argentina
Departamento de Matemáticas y Estadística, Universidad Torcuato di Tella, Avenida Figueroa Alcorta 7350, 1428, Ciudad Autónoma de Buenos Aires, Argentina
CONICET, Argentina
Palabras clave:Composition operators; Differentiation operators; Holomorphy types; Hypercyclic operators; Non-convolution operators; Strongly mixing operators
Año:2018
Volumen:468
Número:2
Página de inicio:622
Página de fin:641
DOI: http://dx.doi.org/10.1016/j.jmaa.2018.08.017
Título revista:Journal of Mathematical Analysis and Applications
Título revista abreviado:J. Math. Anal. Appl.
ISSN:0022247X
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v468_n2_p622_Muro

Referencias:

  • Aron, R.M., Weakly uniformly continuous and weakly sequentially continuous entire functions (1979) Advances in Holomorphy, Proc. Sem. Univ. Fed. Rio de Janeiro, Rio de Janeiro, 1977, North-Holland Math. Stud., 34, pp. 47-66. , North-Holland Amsterdam
  • Aron, R.M., Berner, P.D., A Hahn–Banach extension theorem for analytic mappings (1978) Bull. Soc. Math. France, 106 (1), pp. 3-24
  • Aron, R.M., Bés, J., Hypercyclic differentiation operators (1999) Function Spaces, Edwardsville, IL, 1998, Contemp. Math., 232, pp. 39-46. , Amer. Math. Soc. Providence, RI
  • Aron, R.M., Markose, D., Satellite Conference on Infinite Dimensional Function Theory, On universal functions (2004) J. Korean Math. Soc., 41 (1), pp. 65-76
  • Bayart, F., Matheron, É., Mixing operators and small subsets of the circle (2016) J. Reine Angew. Math., 2016 (715), pp. 75-123
  • Bertoloto, F.J., Botelho, G., Fávaro, V.V., Jatobá, A.M., Hypercyclicity of convolution operators on spaces of entire functions (2013) Ann. Inst. Fourier (Grenoble), 63 (4), pp. 1263-1283
  • Birkhoff, G.D., Démonstration d'un théorème élémentaire sur les fonctions entières (1929) C. R. Acad. Sci. Paris, 189, pp. 473-475
  • Bohr, H., A theorem concerning power series (1914) Proc. Lond. Math. Soc., 2 (1), pp. 1-5
  • Bonilla, A., Grosse-Erdmann, K.-G., On a theorem of Godefroy and Shapiro (2006) Integral Equations Operator Theory, 56 (2), pp. 151-162
  • Carando, D., Extendibility of polynomials and analytic functions on lp (2001) Studia Math., 145 (1), pp. 63-73
  • Carando, D., Dimant, V., Muro, S., Hypercyclic convolution operators on Fréchet spaces of analytic functions (2007) J. Math. Anal. Appl., 336 (2), pp. 1324-1340
  • Carando, D., Dimant, V., Muro, S., Coherent sequences of polynomial ideals on Banach spaces (2009) Math. Nachr., 282 (8), pp. 1111-1133
  • Carando, D., Dimant, V., Muro, S., Holomorphic functions and polynomial ideals on Banach spaces (2012) Collect. Math., 63 (1), pp. 71-91
  • Carando, D., Galicer, D., The symmetric Radon–Nikodym property for tensor norms (2011) J. Math. Anal. Appl., 375 (2), pp. 553-565
  • Dimant, V., Galindo, P., Maestre, M., Zalduendo, I., Integral holomorphic functions (2004) Studia Math., 160 (1), pp. 83-99
  • Dineen, S., Holomorphy types on a Banach space (1971) Studia Math., 39, pp. 241-288
  • Dwyer, T.A.W., III, Partial differential equations in Fischer–Fock spaces for the Hilbert–Schmidt holomorphy type (1971) Bull. Amer. Math. Soc., 77, pp. 725-730
  • Fávaro, V.V., Jatobá, A.M., Holomorphy types and spaces of entire functions of bounded type on Banach spaces (2009) Czechoslovak Math. J., 59 (4), pp. 909-927
  • Fávaro, V.V., Jatobá, A.M., Hypercyclicity, existence and approximation results for convolution operators on spaces of entire functions (2018), arXiv preprint; Fávaro, V.V., Mujica, J., Hypercyclic convolution operators on spaces of entire functions (2016) J. Operator Theory, 76 (1), pp. 141-158
  • Fávaro, V.V., Mujica, J., Convolution operators on spaces of entire functions (2018) Math. Nachr., 291 (1), pp. 41-54
  • Fernández, G., Hallack, A.A., Remarks on a result about hypercyclic non-convolution operators (2005) J. Math. Anal. Appl., 309 (1), pp. 52-55
  • Floret, K., Minimal ideals of n-homogeneous polynomials on Banach spaces (2001) Results Math., 39 (3-4), pp. 201-217
  • Floret, K., On ideals of n-homogeneous polynomials on Banach spaces (2002) Topological Algebras with Applications to Differential Geometry and Mathematical Physics, Athens, 1999, pp. 19-38. , Univ. Athens Athens
  • Godefroy, G., Shapiro, J.H., Operators with dense, invariant, cyclic vector manifolds (1991) J. Funct. Anal., 98 (2), pp. 229-269
  • Gowers, W.T., Maurey, B., The unconditional basic sequence problem (1993) J. Amer. Math. Soc., 6 (4), pp. 851-874
  • Gupta, C.P., On the Malgrange theorem for nuclearly entire functions of bounded type on a Banach space (1970) Nederl. Akad. Wetensch. Proc. Ser. A73 = Indag. Math., 32, pp. 356-358
  • Gupta, M., Mundayadan, A., q-Frequently hypercyclic operators (2015) Banach J. Math. Anal., 9 (2), pp. 114-126
  • Hallack, A.A., Hypercyclicity for translations through Runge's theorem (2007) Bull. Korean Math. Soc., 44 (1), pp. 117-123
  • León-Saavedra, F., Romero-de la Rosa, P., Fixed points and orbits of non-convolution operators (2014) Fixed Point Theory Appl., 2014 (1)
  • Lindenstrauss, J., Tzafriri, L., Classical Banach Spaces I (1979), Springer-Verlag; MacLane, G.R., Sequences of derivatives and normal families (1952) J. Anal. Math., 2, pp. 72-87
  • Murillo-Arcila, M., Peris, A., Strong mixing measures for linear operators and frequent hypercyclicity (2013) J. Math. Anal. Appl., 398 (2), pp. 462-465
  • Muro, S., On algebras of holomorphic functions of a given type (2012) J. Math. Anal. Appl., 389 (2), pp. 792-811
  • Muro, S., Pinasco, D., Savransky, M., Strongly mixing convolution operators on Fréchet spaces of holomorphic functions (2014) Integral Equations Operator Theory, 80 (4), pp. 453-468
  • Muro, S., Pinasco, D., Savransky, M., Hypercyclic behavior of some non-convolution operators on H(CN) (2017) J. Operator Theory, 77 (1), pp. 39-59
  • Nachbin, L., Topology on Spaces of Holomorphic Mappings (1969) Ergeb. Math. Grenzgeb., Band 47. , Springer-Verlag New York Inc. New York
  • Petersson, H., Hypercyclic convolution operators on entire functions of Hilbert–Schmidt holomorphy type (2001) Ann. Math. Blaise Pascal, 8 (2), pp. 107-114
  • Petersson, H., Hypercyclic subspaces for Fréchet space operators (2006) J. Math. Anal. Appl., 319 (2), pp. 764-782
  • Petersson, H., Supercyclic and hypercyclic non-convolution operators (2006) J. Operator Theory, pp. 135-151

Citas:

---------- APA ----------
Muro, S., Pinasco, D. & Savransky, M. (2018) . Dynamics of non-convolution operators and holomorphy types. Journal of Mathematical Analysis and Applications, 468(2), 622-641.
http://dx.doi.org/10.1016/j.jmaa.2018.08.017
---------- CHICAGO ----------
Muro, S., Pinasco, D., Savransky, M. "Dynamics of non-convolution operators and holomorphy types" . Journal of Mathematical Analysis and Applications 468, no. 2 (2018) : 622-641.
http://dx.doi.org/10.1016/j.jmaa.2018.08.017
---------- MLA ----------
Muro, S., Pinasco, D., Savransky, M. "Dynamics of non-convolution operators and holomorphy types" . Journal of Mathematical Analysis and Applications, vol. 468, no. 2, 2018, pp. 622-641.
http://dx.doi.org/10.1016/j.jmaa.2018.08.017
---------- VANCOUVER ----------
Muro, S., Pinasco, D., Savransky, M. Dynamics of non-convolution operators and holomorphy types. J. Math. Anal. Appl. 2018;468(2):622-641.
http://dx.doi.org/10.1016/j.jmaa.2018.08.017