论文标题
最终在完整的局部凸空间之间恒定交织的线性图
Eventually constant intertwining linear maps between complete locally convex spaces
论文作者
论文摘要
从辛克莱（Sinclair）1976年的工作{\ IT线性操作员的自动连续性}，剑桥大学出版社（1976），关于Banach空间上线性操作员自动连续性的自动连续性，我们证明，相互交织的连续线性映射的序列最终与固定线性映射的分离空间相对于固定的线性映射持续不变。我们的证明使用滑行驼峰论证。 We also consider aspects of continuity of linear functions between locally convex spaces and prove that such that a linear function $T$ from the locally convex space $X$ to the locally convex space $Y$ is continuous whenever the separating space $G(T)$ is the zero vector in $Y$ and for which $X$ and $Y$ satisfy conditions for a closed graph theorem.
Starting from Sinclair's 1976 work {\it Automatic Continuity of Linear Operators}, Cambridge University Press, (1976), on automatic continuity of linear operators on Banach spaces, we prove that sequences of intertwining continuous linear maps are eventually constant with respect to the separating space of a fixed linear map. Our proof uses a gliding hump argument. We also consider aspects of continuity of linear functions between locally convex spaces and prove that such that a linear function $T$ from the locally convex space $X$ to the locally convex space $Y$ is continuous whenever the separating space $G(T)$ is the zero vector in $Y$ and for which $X$ and $Y$ satisfy conditions for a closed graph theorem.
