| Title:
|
Homomorphisms between algebras of holomorphic functions in infinite dimensional spaces (English) |
| Author:
|
Condori, Luciano O. |
| Author:
|
Lourenço, M. Lilian |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
132 |
| Issue:
|
3 |
| Year:
|
2007 |
| Pages:
|
237-241 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is shown that a homomorphism between certain topological algebras of holomorphic functions is continuous if and only if it is a composition operator. (English) |
| Keyword:
|
holomorphic function |
| Keyword:
|
continuous homomorphism |
| MSC:
|
46E15 |
| MSC:
|
46E50 |
| MSC:
|
46G20 |
| MSC:
|
47B33 |
| idZBL:
|
Zbl 1174.46021 |
| idMR:
|
MR2355656 |
| DOI:
|
10.21136/MB.2007.134121 |
| . |
| Date available:
|
2009-09-24T22:31:21Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134121 |
| . |
| Reference:
|
[1] L. O. Condori, M. L. Lourenço: Continuous homomorphism between topological algebras of holomorphic germs.Rocky Moutain J. Math. 36(5) (2006), 1457–1469. MR 2285294, 10.1216/rmjm/1181069376 |
| Reference:
|
[2] S. Dineen: Complex Analysis on Infinite Dimensional Spaces.Springer, 1999. Zbl 1034.46504, MR 1705327 |
| Reference:
|
[3] J. Horvath: Topological Vector Spaces and Distributions Vol. 1.Addison-Wesley, 1966. MR 0205028 |
| Reference:
|
[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. Zbl 0415.46020, MR 0520668 |
| Reference:
|
[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. Zbl 0401.46024, MR 0555871 |
| Reference:
|
[6] J. Mujica: Complex Analysis in Banach Spaces.Math. Stud. Vol. 120, North-Holland, 1986. Zbl 0586.46040, MR 0842435 |
| Reference:
|
[7] L. Nachbin: On the topology of the space of all holomorphic functions on a given open subset.Indag. Math. 29 (1967), 366–368. Zbl 0147.11402, MR 0215066 |
| Reference:
|
[8] L. Nachbin: Topics on Topological Vector Spaces.Textos de Métodos Matemáticos da Universidade Federal do Rio de Janeiro, 1974. |
| Reference:
|
[9] B. Tsirelson: Not every Banach space contains an imbedding of $\ell _p$ or $\text{c}_0$.Funct. Anal. Appl. 8 (1974), 138–144. 10.1007/BF01078599 |
| . |
