A remark about the embedding
, with
, in Frechet spaces
Abstract
In a recentpaper by Aron-Moraes-Ryan [2], it is proved that when E is a complex Banach space, F is a closed subspace of E and U is a balanced open subset of E, then the mapping
where 𝜋 is the canonical mapping from E onto
, is a topological isomorphism from
onto a closed subspace of
, where
. The aim of this remark is to show that the same result is true, with
for Fréchet spaces, and with
for Fréchet-Schwartz spaces. Also we prove that this result is not true, with
for some Fréchet-Montel spaces and with
for some nuclear Fréchet spaces.
![f ∈ H(𝜋(U)) → f ○ 𝜋 ∈ H(U)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/a632d969127c702840ace56b78c7a56d.png)
![E/F](http://siba-ese.unile.it/plugins/generic/latexRender/cache/f7c407ec4afd828de4ea6435084247f5.png)
![(H(𝜋(U)),τ)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/bbe88242b485aacc13996bc03a166ea1.png)
![(H(U),τ](http://siba-ese.unile.it/plugins/generic/latexRender/cache/64044d8bfbb45753ba9c80b36ad88bff.png)
![τ = τ<sub>0</sub>,τ_ω](http://siba-ese.unile.it/plugins/generic/latexRender/cache/6bcc3b071a756561c806d47696c570a9.png)
![τ<sub>0</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/244cc81d2902f68a73b22ff9b36b7301.png)
![τ_omega](http://siba-ese.unile.it/plugins/generic/latexRender/cache/a10d7307d0c724e8d5ffc8067c4df8f0.png)
![τ_ω](http://siba-ese.unile.it/plugins/generic/latexRender/cache/51231208544447905d62bb08e98c910b.png)
![τ_δ](http://siba-ese.unile.it/plugins/generic/latexRender/cache/394b7b2e02e51cfc4b777119a3958b3d.png)
DOI Code:
10.1285/i15900932v9n2p217
Full Text: PDF