论文标题
在某些核特雷希特空间的电源序列子空间
On Power Series Subspaces of Certain Nuclear Frechet Spaces
论文作者
论文摘要
从理论上讲，$δ（e）$和大致的直径尺寸，$δ（e）$ $ e $的$ e $ e $的大量核fréchet空间是从理论上设置的，在电源序列的相应不变性空间$λ_{1}（\ varepsilon）$和$λ_ {\λ_ {\ necoments $ vareps（\ vareps）之间$ \ varepsilon $。 Aytuna等人，\ cite {akt2}，证明$ e $包含一个补充子空间，同构为$λ_ {\ infty}（\ varepsilon）$提供的$δ（e）=δ（e）=δ 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 $Λ_{1}(\varepsilon)$.
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 $Λ_{1}(\varepsilon)$.
