论文标题
在某些本地凸FK空间
On some locally convex FK spaces
论文作者
论文摘要
我们为矢量空间提供必要的和/或足够的条件，即真实序列的$ v $是一个fréchet空间，使每个坐标图是连续的，也就是说是本地凸出的FK空间。 特别是，我们表明，如果$ c_ {00}（\ Mathcal {i}）\ subseteq v \ subseteq \ ell_ \ ell_ \ infty（\ Mathcal {i}）$ for某些理想的$ \ nathcal {i} $ in $ v $ in Iff inf and n inf Iff infins，则为某些理想的$ \ nathcal {i} $ in Iff inf infind If，每个无限子集不属于$ \ Mathcal {i} $的ω$。
We provide necessary and/or sufficient conditions on vector spaces $V$ of real sequences to be a Fréchet space such that each coordinate map is continuous, that is, to be a locally convex FK space. In particular, we show that if $c_{00}(\mathcal{I})\subseteq V\subseteq \ell_\infty(\mathcal{I})$ for some ideal $\mathcal{I}$ on $ω$, then $V$ is a locally convex FK space if and only if there exists an infinite set $S\subseteq ω$ for which every infinite subset does not belong to $\mathcal{I}$.
