无连续范数的fr空间的不变子空间

Q. Menet
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引用次数: 0

摘要

设$(X,(p_j))$是一个具有Schauder基且无连续范数的Frechet空间,其中$(p_j)$是引起$X$拓扑的半模的递增序列。证明了$X$满足不变子空间性质当且仅当存在$j_0\ ge1 $使得$\ kerp_ {j+1}$在$\ kerp_ {j}$中对每一个$j\ gej_0 $具有有限余维数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Invariant subspaces for Fréchet spaces without continuous norm
Let $(X,(p_j))$ be a Frechet space with a Schauder basis and without continuous norm, where $(p_j)$ is an increasing sequence of seminorms inducing the topology of $X$. We show that $X$ satisfies the Invariant Subspace Property if and only if there exists $j_0\ge 1$ such that $\ker p_{j+1}$ is of finite codimension in $\ker p_{j}$ for every $j\ge j_0$.
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