Geodesic
Every Separable Complex Fréchet Space with a Continuous Norm is Isomorphic to a Space of Holomorphic Functions
Canadian mathematical bulletin, Tome 64 (2021) no. 1, pp. 8-12

Voir la notice de l'article provenant de la source Cambridge

DOI

Extending a result of Mashreghi and Ransford, we prove that every complex separable infinite-dimensional Fréchet 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 Fréchet spaces of holomorphic functions without the bounded approximation.
DOI : 10.4153/S000843952000017X
Mots-clés : Spaces of holomorphic functions, Fréchet spaces, continuous norm, bounded approximation property 
Bonet, José. Every Separable Complex Fréchet Space with a Continuous Norm is Isomorphic to a Space of Holomorphic Functions. Canadian mathematical bulletin, Tome 64 (2021) no. 1, pp. 8-12. doi: 10.4153/S000843952000017X
@article{10_4153_S000843952000017X,
     author = {Bonet, Jos\'e},
     title = {Every {Separable} {Complex} {Fr\'echet} {Space} with a {Continuous} {Norm} is {Isomorphic} to a {Space} of {Holomorphic} {Functions}},
     journal = {Canadian mathematical bulletin},
     pages = {8--12},
     year = {2021},
     volume = {64},
     number = {1},
     doi = {10.4153/S000843952000017X},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S000843952000017X/}
}
TY  - JOUR
AU  - Bonet, José
TI  - Every Separable Complex Fréchet Space with a Continuous Norm is Isomorphic to a Space of Holomorphic Functions
JO  - Canadian mathematical bulletin
PY  - 2021
SP  - 8
EP  - 12
VL  - 64
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/S000843952000017X/
DO  - 10.4153/S000843952000017X
ID  - 10_4153_S000843952000017X
ER  - 
%0 Journal Article
%A Bonet, José
%T Every Separable Complex Fréchet Space with a Continuous Norm is Isomorphic to a Space of Holomorphic Functions
%J Canadian mathematical bulletin
%D 2021
%P 8-12
%V 64
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/S000843952000017X/
%R 10.4153/S000843952000017X
%F 10_4153_S000843952000017X

Cité par Sources :