Every Separable Complex Frechet Space with a Continuous Norm is Isomorphic to a Space of Holomorphic Functions

被引：1

作者：

Bonet, Jose ^{[1
]}

机构：

[1] Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada IUMPA, E-46071 Valencia, Spain

来源：

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2021年 / 64卷 / 01期

关键词：

Spaces of holomorphic functions; Frechet spaces; continuous norm; bounded approximation property; C-INFINITY-FUNCTIONS;

D O I：

10.4153/S000843952000017X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Extending a result of Mashreghi and Ransford, we prove that every complex separable infinite-dimensional Frechet space with a continuous norm is isomorphic to a space continuously included in a space of holomorphic functions on the unit disc or the complex plane, which contains the polynomials as a dense subspace. As a consequence, we deduce the existence of nuclear Frechet spaces of holomorphic functions without the bounded approximation.

引用

页码：8 / 12

页数：5