Geodesic
Homomorphisms between algebras of holomorphic functions in infinite dimensional spaces
Mathematica Bohemica, Tome 132 (2007) no. 3, pp. 237-241

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
It is shown that a homomorphism between certain topological algebras of holomorphic functions is continuous if and only if it is a composition operator.
It is shown that a homomorphism between certain topological algebras of holomorphic functions is continuous if and only if it is a composition operator.
DOI : 10.21136/MB.2007.134121
Classification : 46E15, 46E50, 46G20, 47B33
Keywords: holomorphic function; continuous homomorphism 
Condori, Luciano O.; Lourenço, M. Lilian. Homomorphisms between algebras of holomorphic functions in infinite dimensional spaces. Mathematica Bohemica, Tome 132 (2007) no. 3, pp. 237-241. doi: 10.21136/MB.2007.134121
@article{10_21136_MB_2007_134121,
     author = {Condori, Luciano O. and Louren\c{c}o, M. Lilian},
     title = {Homomorphisms between algebras of holomorphic functions in infinite dimensional spaces},
     journal = {Mathematica Bohemica},
     pages = {237--241},
     year = {2007},
     volume = {132},
     number = {3},
     doi = {10.21136/MB.2007.134121},
     mrnumber = {2355656},
     zbl = {1174.46021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2007.134121/}
}
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
SP  - 237
EP  - 241
VL  - 132
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2007.134121/
DO  - 10.21136/MB.2007.134121
LA  - en
ID  - 10_21136_MB_2007_134121
ER  - 
%0 Journal Article
%A Condori, Luciano O.
%A Lourenço, M. Lilian
%T Homomorphisms between algebras of holomorphic functions in infinite dimensional spaces
%J Mathematica Bohemica
%D 2007
%P 237-241
%V 132
%N 3
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2007.134121/
%R 10.21136/MB.2007.134121
%G en
%F 10_21136_MB_2007_134121

[1] L. O. Condori, M. L. Lourenço: Continuous homomorphism between topological algebras of holomorphic germs. Rocky Moutain J. Math. 36(5) (2006), 1457–1469. | DOI | MR

[2] S. Dineen: Complex Analysis on Infinite Dimensional Spaces. Springer, 1999. | MR | Zbl

[3] J. Horvath: Topological Vector Spaces and Distributions Vol. 1. Addison-Wesley, 1966. | MR

[4] J. M. Isidro: Characterization of the spectrum of some topological algebras of holomorphic functions. Advances in Holomorphy, (ed. J.A. Barroso), North-Holland, 1979, pp. 407–416. | MR | Zbl

[5] J. Mujica: The Oka-Weil theorem in locally convex spaces with the approximation property. Séminaire Paul Krée 1977/1978. Institute Henri Poincaré, Paris, 1979. | MR | Zbl

[6] J. Mujica: Complex Analysis in Banach Spaces. Math. Stud. Vol. 120, North-Holland, 1986. | MR | Zbl

[7] L. Nachbin: On the topology of the space of all holomorphic functions on a given open subset. Indag. Math. 29 (1967), 366–368. | MR | Zbl

[8] L. Nachbin: Topics on Topological Vector Spaces. Textos de Métodos Matemáticos da Universidade Federal do Rio de Janeiro, 1974.

[9] B. Tsirelson: Not every Banach space contains an imbedding of $\ell _p$ or $\text{c}_0$. Funct. Anal. Appl. 8 (1974), 138–144. | DOI

Cité par Sources :