论文标题
不连续规范的Fréchet空间的不变子空间
Invariant subspaces for Fréchet spaces without continuous norm
论文作者
论文摘要
令$（x，（p_j））$为具有Schauder基础的Fréchet空间，没有连续的规范，其中$（p_j）$是越来越多的eminorms序列，诱导了$ x $的拓扑。我们表明，$ x $仅当存在$ j_0 \ ge 1 $时，就可以满足不变的子空间属性，以使每一个$ \ ker p_ {j} $ in $ \ ker p_ {j} $中的$ \ ker p_ {j+1} $对于每个$ j \ ge j_0 $。
Let $(X,(p_j))$ be a Fréchet 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 $j\ge j_0$.
