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arXiv · 2210.13593

On Power Series Subspaces of Certain Nuclear Frechet Spaces

Nazlı Doğan
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Abstract

The diametral dimension, $Δ(E)$, and the approximate diametral dimension, $δ(E)$ of an element $E$ of a large class of nuclear Fréchet spaces are set theoretically between the corresponding invariant of power series spaces $Λ_{1}(\varepsilon)$ and $Λ_{\infty}(\varepsilon)$ for some exponent sequence $\varepsilon$. Aytuna et al., \cite{AKT2}, proved that $E$ contains a complemented subspace which is isomorphic to $Λ_{\infty}(\varepsilon)$ provided $Δ(E)=Δ( Λ_{\infty}(\varepsilon))$ and $\varepsilon$ is stable. In this article, we will consider the other extreme case and we proved that in this large family, there exist nuclear Fréchet spaces, even regular nuclear Köthe spaces, satisfying $Δ(E)=Δ(Λ_{1}(\varepsilon))$ such that there is no subspace of $E$ which is isomorphic to $Λ_{1}(\varepsilon)$.

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Nazlı Doğan. 2022-10-24. On Power Series Subspaces of Certain Nuclear Frechet Spaces. https://arxiv.org/abs/2210.13593

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