Homomorphisms between algebras of holomorphic functions in infinite dimensional spaces

Luciano O. Condori; M. Lilian Lourenço

Mathematica Bohemica (2007)

  • Volume: 132, Issue: 3, page 237-241
  • ISSN: 0862-7959

Abstract

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It is shown that a homomorphism between certain topological algebras of holomorphic functions is continuous if and only if it is a composition operator.

How to cite

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Condori, Luciano O., and Lourenço, M. Lilian. "Homomorphisms between algebras of holomorphic functions in infinite dimensional spaces." Mathematica Bohemica 132.3 (2007): 237-241. <http://eudml.org/doc/250256>.

@article{Condori2007,
abstract = {It is shown that a homomorphism between certain topological algebras of holomorphic functions is continuous if and only if it is a composition operator.},
author = {Condori, Luciano O., Lourenço, M. Lilian},
journal = {Mathematica Bohemica},
keywords = {holomorphic function; continuous homomorphism; holomorphic function; continuous homomorphism},
language = {eng},
number = {3},
pages = {237-241},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Homomorphisms between algebras of holomorphic functions in infinite dimensional spaces},
url = {http://eudml.org/doc/250256},
volume = {132},
year = {2007},
}

TY - JOUR
AU - Condori, Luciano O.
AU - Lourenço, M. Lilian
TI - Homomorphisms between algebras of holomorphic functions in infinite dimensional spaces
JO - Mathematica Bohemica
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 132
IS - 3
SP - 237
EP - 241
AB - It is shown that a homomorphism between certain topological algebras of holomorphic functions is continuous if and only if it is a composition operator.
LA - eng
KW - holomorphic function; continuous homomorphism; holomorphic function; continuous homomorphism
UR - http://eudml.org/doc/250256
ER -

References

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  1. Continuous homomorphism between topological algebras of holomorphic germs, Rocky Moutain J. Math. 36(5) (2006), 1457–1469. (2006) MR2285294
  2. Complex Analysis on Infinite Dimensional Spaces, Springer, 1999. (1999) Zbl1034.46504MR1705327
  3. Topological Vector Spaces and Distributions Vol. 1, Addison-Wesley, 1966. (1966) MR0205028
  4. Characterization of the spectrum of some topological algebras of holomorphic functions, Advances in Holomorphy, (ed. J.A. Barroso), North-Holland, 1979, pp. 407–416. (1979) Zbl0415.46020MR0520668
  5. The Oka-Weil theorem in locally convex spaces with the approximation property, Séminaire Paul Krée 1977/1978. Institute Henri Poincaré, Paris, 1979. (1979) Zbl0401.46024MR0555871
  6. Complex Analysis in Banach Spaces, Math. Stud. Vol. 120, North-Holland, 1986. (1986) Zbl0586.46040MR0842435
  7. On the topology of the space of all holomorphic functions on a given open subset, Indag. Math. 29 (1967), 366–368. (1967) Zbl0147.11402MR0215066
  8. Topics on Topological Vector Spaces, Textos de Métodos Matemáticos da Universidade Federal do Rio de Janeiro, 1974. (1974) 
  9. Not every Banach space contains an imbedding of p or c 0 , Funct. Anal. Appl. 8 (1974), 138–144. (1974) 

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