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

Publicacions Matemàtiques (1995)

- Volume: 39, Issue: 1, page 71-88
- ISSN: 0214-1493

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topMinh 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 -

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