Navegar

Colección

Datos Estadísticas

Artículo

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:

The Cluster Value Theorem is known for being a weak version of the classical Corona Theorem. Given a Banach space X, we study the Cluster Value Problem for the ball algebra Au(BX), the Banach algebra of all uniformly continuous holomorphic functions on the unit ball BX; and also for the Fréchet algebra Hb(X) of holomorphic functions of bounded type on X (more generally, for Hb(U), the algebra of holomorphic functions of bounded type on a given balanced open subset U⊂X). We show that Cluster Value Theorems hold for all of these algebras whenever the dual of X has the bounded approximation property. These results are an important advance in this problem, since the validity of these theorems was known only for trivial cases (where the spectrum is formed only by evaluation functionals) and for the infinite dimensional Hilbert space. As a consequence, we obtain weak analytic Nullstellensatz theorems and several structural results for the spectrum of these algebras. © 2017 Elsevier Inc.

Registro:

Documento: Artículo
Título:Cluster values for algebras of analytic functions
Autor:Carando, D.; Galicer, D.; Muro, S.; Sevilla-Peris, P.
Filiación:Departamento de Matemática - PAB I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, (1428), Argentina
Instituto de Investigaciones Matemáticas Luis A. Santaló (IMAS) - CONICET UBA, Argentina
Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de de València, Cmno Vera s/n, Valencia, 46022, Spain
Palabras clave:Analytic functions of bounded type; Ball algebra; Cluster value problem; Corona Theorem; Fiber; Spectrum
Año:2018
Volumen:329
Página de inicio:157
Página de fin:173
DOI: http://dx.doi.org/10.1016/j.aim.2017.08.030
Título revista:Advances in Mathematics
Título revista abreviado:Adv. Math.
ISSN:00018708
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00018708_v329_n_p157_Carando

Referencias:

  • Acosta, M.D., Lourenço, M.L., Shilov boundary for holomorphic functions on some classical Banach spaces (2007) Studia Math., 179 (1), pp. 27-39
  • Albiac, F., Kalton, N.J., Topics in Banach Space Theory (2006) Grad. Texts in Math., 233. , Springer New York
  • Arens, R., Dense inverse limit rings (1958) Michigan Math. J., 5 (2), pp. 169-182
  • Aron, R.M., Carando, D., Gamelin, T.W., Lassalle, S., Maestre, M., Cluster values of analytic functions on a Banach space (2012) Math. Ann., 353 (2), pp. 293-303
  • Aron, R.M., Carando, D., Lassalle, S., Maestre, M., Cluster values of holomorphic functions of bounded type (2016) Trans. Amer. Math. Soc., 368, pp. 2355-2369
  • Aron, R.M., Cole, B.J., Gamelin, T.W., Spectra of algebras of analytic functions on a Banach space (1991) J. Reine Angew. Math., 415, pp. 51-93
  • Aron, R.M., Cole, B.J., Gamelin, T.W., Weak-star continuous analytic functions (1995) Canad. J. Math., 47 (4), pp. 673-683
  • Aron, R., Falcó, J., García, D., Maestre, M., Analytic structure in fibers, Oberwolfach Preprints; Borel-Mathurin, L., Isomorphismes non linéaires entre espaces de Banach (2010), PhD thesis, Paris 6; Carando, D., García, D., Maestre, M., Homomorphisms and composition operators on algebras of analytic functions of bounded type (2005) Adv. Math., 197 (2), pp. 607-629
  • Carando, D., García, D., Maestre, M., Sevilla-Peris, P., On the spectra of algebras of analytic functions (2012) Topics in Complex Analysis and Operator Theory, pp. 165-198
  • Carando, D., Muro, S., Envelopes of holomorphy and extension of functions of bounded type (2012) Adv. Math., 229 (3), pp. 2098-2121
  • Carleson, L., Interpolations by bounded analytic functions and the corona problem (1962) Ann. of Math., pp. 547-559
  • Casazza, P.G., Approximation properties (2001) Handbook of the Geometry of Banach Spaces, vol. 1, pp. 271-316
  • Deville, R., Godefroy, G., Zizler, V., Smoothness and Renormings in Banach Spaces (1993) Pitman Monogr. Surv. Pure Appl. Math., 64. , Longman Scientific & Technical Harlow copublished in the United States with John Wiley & Sons, Inc. New York
  • Dineen, S., Complex Analysis on Infinite Dimensional Spaces (1999) Springer Monogr. Math., , Springer London
  • Johnson, W.B., Castillo, S.O., The cluster value problem for Banach spaces (2014) Illinois J. Math., 58 (2), pp. 405-412
  • Johnson, W., Castillo, S.O., The cluster value problem in spaces of continuous functions (2015) Proc. Amer. Math. Soc., 143 (4), pp. 1559-1568
  • Lindenstrauss, J., Tzafriri, L., Classical Banach Spaces (1973) Lecture Notes in Math., 338. , Springer-Verlag Berlin
  • Moltó, A., Montesinos, V., Troyanski, S., On quasi-denting points, denting faces and the geometry of the unit ball of d(w,1) (1994) Arch. Math., 63 (1), pp. 45-55
  • Moltó, A., Orihuela, J., Troyanski, S., Valdivia, M., Kadec and Krein–Milman properties (2000) C. R. Acad. Sci., Ser. I Math., 331 (6), pp. 459-464
  • Mujica, J., Holomorphic functions and domains of holomorphy in finite and infinite dimensions, XI (1986) Complex Analysis in Banach Spaces, North-Holl. Math. Stud., vol. 120, Notas Mat., 107. , North-Holland Amsterdam/New York/Oxford
  • Schark, I.J., Maximal ideals in an algebra of bonded analytic functions (1961) J. Math. Mech., 10 (5), pp. 735-746
  • Sibony, N., Prolongement analytique des fonctions holomorphes bornées (1974) Séminaire Pierre Lelong (Analyse) Année 1972–1973, pp. 44-66. , Springer

Citas:

---------- APA ----------
Carando, D., Galicer, D., Muro, S. & Sevilla-Peris, P. (2018) . Cluster values for algebras of analytic functions. Advances in Mathematics, 329, 157-173.
http://dx.doi.org/10.1016/j.aim.2017.08.030
---------- CHICAGO ----------
Carando, D., Galicer, D., Muro, S., Sevilla-Peris, P. "Cluster values for algebras of analytic functions" . Advances in Mathematics 329 (2018) : 157-173.
http://dx.doi.org/10.1016/j.aim.2017.08.030
---------- MLA ----------
Carando, D., Galicer, D., Muro, S., Sevilla-Peris, P. "Cluster values for algebras of analytic functions" . Advances in Mathematics, vol. 329, 2018, pp. 157-173.
http://dx.doi.org/10.1016/j.aim.2017.08.030
---------- VANCOUVER ----------
Carando, D., Galicer, D., Muro, S., Sevilla-Peris, P. Cluster values for algebras of analytic functions. Adv. Math. 2018;329:157-173.
http://dx.doi.org/10.1016/j.aim.2017.08.030