Abstract and Applied Analysis

Homomorphisms between Algebras of Holomorphic Functions

Verónica Dimant, Domingo García, Manuel Maestre, and Pablo Sevilla-Peris

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


For two complex Banach spaces X and Y , in this paper, we study the generalized spectrum b ( X , Y ) of all nonzero algebra homomorphisms from b ( X ) , the algebra of all bounded type entire functions on X , into b ( Y ) . We endow b ( X , Y ) with a structure of Riemann domain over ( X * , Y * ) whenever X is symmetrically regular. The size of the fibers is also studied. Following the philosophy of (Aron et al., 1991), this is a step to study the set b , ( X , B Y ) of all nonzero algebra homomorphisms from b ( X ) into ( B Y ) of bounded holomorphic functions on the open unit ball of Y and ( B X , B Y ) of all nonzero algebra homomorphisms from ( B X ) into ( B Y ) .

Article information

Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 612304, 12 pages.

First available in Project Euclid: 2 October 2014

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Dimant, Verónica; García, Domingo; Maestre, Manuel; Sevilla-Peris, Pablo. Homomorphisms between Algebras of Holomorphic Functions. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 612304, 12 pages. doi:10.1155/2014/612304. https://projecteuclid.org/euclid.aaa/1412278777

Export citation


  • D. Carando, D. García, and M. Maestre, “Homomorphisms and composition operators on algebras of analytic functions of bounded type,” Advances in Mathematics, vol. 197, no. 2, pp. 607–629, 2005.
  • R. M. Aron, B. J. Cole, and T. W. Gamelin, “Spectra of algebras of analytic functions on a Banach space,” Journal für die Reine und Angewandte Mathematik, vol. 415, pp. 51–93, 1991.
  • R. M. Aron, P. Galindo, D. García, and M. Maestre, “Regularity and algebras of analytic functions in infinite dimensions,” Transactions of the American Mathematical Society, vol. 348, no. 2, pp. 543–559, 1996.
  • S. Dineen, Complex Analysis on Infinite-Dimensional Spaces, Springer Monographs in Mathematics, Springer, London, UK, 1999.
  • M. J. Beltrán, “Spectra of weighted (LB)-algebras of entire functions on Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 387, no. 2, pp. 604–617, 2012.
  • D. Carando, D. García, M. Maestre, and P. Sevilla-Peris, “A Riemann manifold structure of the spectra of weighted algebras of holomorphic functions,” Topology, vol. 48, no. 2–4, pp. 54–65, 2009.
  • D. Carando and P. Sevilla-Peris, “Spectra of weighted algebras of holomorphic functions,” Mathematische Zeitschrift, vol. 263, no. 4, pp. 887–902, 2009.
  • R. M. Aron and P. D. Berner, “A Hahn-Banach extension theorem for analytic mappings,” Bulletin de la Société Mathématique de France, vol. 106, no. 1, pp. 3–24, 1978.
  • A. M. Davie and T. W. Gamelin, “A theorem on polynomial-star approximation,” Proceedings of the American Mathematical Society, vol. 106, no. 2, pp. 351–356, 1989.
  • J. Mujica, Complex Analysis in Banach Spaces, vol. 120 of North-Holland Mathematics Studies, North-Holland, Amsterdam, The Netherlands, Holomorphic functions and domains of holomorphy in finite and infinite dimensions, Notas de Matemática [Mathematical Notes], 107, 1986.
  • J. A. Barroso, M. C. Matos, and L. Nachbin, “On holomorphy versus linearity in classifying locally convex spaces,” in Infinite Dimensional Holomorphy and Applications, vol. 12 of North-Holland Mathematics Studies, pp. 31–74, North-Holland, Amsterdam, The Netherlands, 1977.
  • S. Lassalle and I. Zalduendo, “To what extent does the dual Banach space ${E}^{'}$ determine the polynomials over $E$?” Arkiv för Matematik, vol. 38, no. 2, pp. 343–354, 2000.
  • D. Carando and S. Muro, “Envelopes of holomorphy and extension of functions of bounded type,” Advances in Mathematics, vol. 229, no. 3, pp. 2098–2121, 2012.
  • C. Boyd and R. A. Ryan, “Bounded weak continuity of homogeneous polynomials at the origin,” Archiv der Mathematik, vol. 71, no. 3, pp. 211–218, 1998.
  • R. Aron and V. Dimant, “Sets of weak sequential continuity for polynomials,” Indagationes Mathematicae, vol. 13, no. 3, pp. 287–299, 2002.
  • R. M. Aron, D. Carando, S. Lassalle, and M. Maestre, “Cluster values of holomorphic functions of bounded typečommentComment on ref. [16?]: Please update the information of this reference, if possible.,” preprint.
  • K.-G. Grosse-Erdmann, “A weak criterion for vector-valued holomorphy,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 136, no. 2, pp. 399–411, 2004.
  • D. Deghoul, “Construction de caractères exceptionnels sur une algèbre de Fréchet,” Comptes Rendus de l'Académie des Sciences., vol. 312, no. 8, pp. 579–580, 1991.
  • J. Mujica, “Linearization of bounded holomorphic mappings on Banach spaces,” Transactions of the American Mathematical Society, vol. 324, no. 2, pp. 867–887, 1991.
  • G. Köthe, Topological Vector Spaces. II, vol. 237 of Grundlehren der Mathematischen Wissenschaften, Springer, New York, NY, USA, 1979. \endinput