Rocky Mountain Journal of Mathematics

Continuous Homomorphisms between Topological Algebras of Holomorphic Germs

Luciano O. Condori and M. Lilian Lourenço

Full-text: Open access

Article information

Rocky Mountain J. Math., Volume 36, Number 5 (2006), 1457-1469.

First available in Project Euclid: 5 June 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46G20: Infinite-dimensional holomorphy [See also 32-XX, 46E50, 46T25, 58B12, 58C10] 32A38: Algebras of holomorphic functions [See also 30H05, 46J10, 46J15] 47B33: Composition operators

Holomorphic germs continuous homomorphisms


Condori, Luciano O.; Lourenço, M. Lilian. Continuous Homomorphisms between Topological Algebras of Holomorphic Germs. Rocky Mountain J. Math. 36 (2006), no. 5, 1457--1469. doi:10.1216/rmjm/1181069376.

Export citation


  • J. Bonet, P. Domanski, M. Lindström and M. S. Ramanujan, Operator spaces containing $c_0$ or $\ell^\infty$, Results Math. 28 (1995), 250-269.
  • S. Dineen, Complex analysis on infinite dimensional spaces, Springer-Verlag, London, 1999.
  • K. Floret, Weakly compact sets, Lecture Notes in Math., vol. 801, Springer, New York, 1978.
  • P. Galindo, M.L. Lourenço and L.A. Moraes, Compact and weakly compact homomorphisms on Fréchet algebras of holomorphic functions, Math. Nachr. 236 (2002), 109-118.
  • M. González and J. Gutiérrez, Schauder type theorems for differentiable and holomorphic mappings, Math. Nachr. 122 (1996), 325-343.
  • --------, Gantmacher type theorems for holomorphic mappings, Math. Nachr. 186 (1997), 131-145.
  • A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955).
  • J. Horvath, Topological vector spaces and distributions, Vol. 1., Addison-Wesley, Massachusetts, 1966.
  • J. Jaramillo and A. Prieto, The weak-polynomial convergence in a Banach space, Proc. Amer. Math. Soc. 118 (1993), 463-468.
  • J. Mujica, Gérmenes holomorfos y funciones holomorfas en espacios de Fréchet, Publicaciones del Depto. de Teoria de Funciones, Universidad de Santiago de Compostela, $N^\ofresco 1$, 1978.
  • --------, Spaces of germs of holomorphic functions, Adv. Math. Suppl. Stud., vol. 4, Academic Press, New York, 1979, pp. 1-41.
  • --------, Ideals of holomorphic functions on Fréchet spaces, in Advances in holomorphy (J.A. Barroso, ed.), North-Holland Publ. Co., Amsterdam, 1979.
  • --------, Complex analysis in Banach spaces, North-Holland Math. Stud. 120, North-Holland, Amsterdam, 1986.
  • --------, Ideals of holomorphic functions on Tsirelson's space, Arch. Math. 76 (2001), 292-298.
  • L. Nachbin, On the topology of the space of all holomorphic function on a given open subset, Indag. Math. 29 (1967), 366-368.
  • O. Nicodemi, Homomorphisms of algebras of germs of holomorphic functions, in Functional analysis, holomorphy and approximation theory (S. Machado, ed.), Lecture Notes in Math., vol. 843, Springer-Verlag, New York, 1981, pp. 534-546.
  • B. Tsirelson, Not every Banach space contains an imbedding of $\ell_p$ or $c_0$, Funct. Anal. Appl. 8 (1974), 138-144.