A remark about the embedding (H(E/F),tau)to(H(E),tau), with tau=tau<sub>0</sub>,tau_omega, in Frechet spaces


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 f ∈ H(𝜋(U)) → f ○ 𝜋 ∈ H(U) where 𝜋 is the canonical mapping from E onto E/F, is a topological isomorphism from (H(𝜋(U)),τ) onto a closed subspace of (H(U),τ, where τ = τ<sub>0</sub>,τ_ω. The aim of this remark is to show that the same result is true, with τ<sub>0</sub> for Fréchet spaces, and with τ_omega for Fréchet-Schwartz spaces. Also we prove that this result is not true, with τ_ω for some Fréchet-Montel spaces and with τ_δ for some nuclear Fréchet spaces.

DOI Code: 10.1285/i15900932v9n2p217

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