论文标题
典型的$ \ ell_p \，$ - $ \，$ space收缩有非平凡的不变子空间吗？
Does a typical $\ell_p\,$-$\,$space contraction have a non-trivial invariant subspace?
论文作者
论文摘要
给定$ {\ Mathcal {b} _ {1}（x）} $上的抛光拓扑$τ$，$ x = \ ell_p $，$ 1 \ le p <\ yftty $或$ x = c_0 $ x = c_0 $上的所有收缩运算符的集合，我们证明与以下问题相关：是否典型$ t \ of ock ock of ofe： {\ Mathcal {B} _ {1}（x）} $在Baire类别中有一个非平凡的不变子空间？换句话说，是否存在密集的$g_δ$ set $ \ mathcal g \ subseteq（{\ nathcal {b} _ {1} _ {1}（x）}，τ）$，使每个$ t \ in \ nathcal in \ nathcal g $都有一个非无聊的不适式subspace吗？我们主要专注于强大的操作员拓扑和强大的$^*$操作员拓扑。
Given a Polish topology $τ$ on ${\mathcal{B}_{1}(X)}$, the set of all contraction operators on $X=\ell_p$, $1\le p<\infty$ or $X=c_0$, we prove several results related to the following question: does a typical $T\in {\mathcal{B}_{1}(X)}$ in the Baire Category sense has a non-trivial invariant subspace? In other words, is there a dense $G_δ$ set $\mathcal G\subseteq ({\mathcal{B}_{1}(X)},τ)$ such that every $T\in\mathcal G$ has a non-trivial invariant subspace? We mostly focus on the Strong Operator Topology and the Strong$^*$ Operator Topology.
