Linear topological invariants of spaces of holomorphic functions in infinite dimension.

Minh Ha, Nguyen, and Hai, Le Mau. "Linear topological invariants of spaces of holomorphic functions in infinite dimension.." Publicacions Matemàtiques 39.1 (1995): 71-88. <http://eudml.org/doc/41220>.

@article{MinhHa1995,
abstract = {It is shown that if E is a Frechet space with the strong dual E* then Hb(E*), the space of holomorphic functions on E* which are bounded on every bounded set in E*, has the property (DN) when E ∈ (DN) and that Hb(E*) ∈ (Ω) when E ∈ (Ω) and either E* has an absolute basis or E is a Hilbert-Frechet-Montel space. Moreover the complementness of ideals J(V) consisting of holomorphic functions on E* which are equal to 0 on V in H(E*) for every nuclear Frechet space E with E ∈ (DN) ∩ (Ω) is stablished when J(V) is finitely generated by continuous polynomials on E*.},
author = {Minh Ha, Nguyen, Hai, Le Mau},
journal = {Publicacions Matemàtiques},
keywords = {Espacios de Fréchet; Espacios de funciones holomorfas; Invariantes topológicos; Topología lineal; Infinito; Fréchet space; strong dual; space of holomorphic functions; property (DN); Hilbert-Fréchet-Montel space; nuclear Fréchet space},
language = {eng},
number = {1},
pages = {71-88},
title = {Linear topological invariants of spaces of holomorphic functions in infinite dimension.},
url = {http://eudml.org/doc/41220},
volume = {39},
year = {1995},
}

TY - JOUR
AU - Minh Ha, Nguyen
AU - Hai, Le Mau
TI - Linear topological invariants of spaces of holomorphic functions in infinite dimension.
JO - Publicacions Matemàtiques
PY - 1995
VL - 39
IS - 1
SP - 71
EP - 88
AB - It is shown that if E is a Frechet space with the strong dual E* then Hb(E*), the space of holomorphic functions on E* which are bounded on every bounded set in E*, has the property (DN) when E ∈ (DN) and that Hb(E*) ∈ (Ω) when E ∈ (Ω) and either E* has an absolute basis or E is a Hilbert-Frechet-Montel space. Moreover the complementness of ideals J(V) consisting of holomorphic functions on E* which are equal to 0 on V in H(E*) for every nuclear Frechet space E with E ∈ (DN) ∩ (Ω) is stablished when J(V) is finitely generated by continuous polynomials on E*.
LA - eng
KW - Espacios de Fréchet; Espacios de funciones holomorfas; Invariantes topológicos; Topología lineal; Infinito; Fréchet space; strong dual; space of holomorphic functions; property (DN); Hilbert-Fréchet-Montel space; nuclear Fréchet space
UR - http://eudml.org/doc/41220
ER -