标题： 冯诺依曼代数上的算子的范围 显示英文标题

标题： The range of operators on von Neumann algebras

摘要： 我们证明对于每个有界线性算子$T:X\to X$，其中$X$是一个冯诺依曼代数的非自反商，算子$T^*$的点谱是非空的（即存在某个$\lambda\in\mathbb C$使得算子$\lambda I-T$不具有稠密的值域）。 特别地，作为应用，我们得到这样的空间不能支持一个拓扑遍历的算子。 显示英文摘要

摘要： We prove that for every bounded linear operator $T:X\to X$, where $X$ is a non-reflexive quotient of a von Neumann algebra, the point spectrum of $T^*$ is non-empty (i.e. for some $\lambda\in\mathbb C$ the operator $\lambda I-T$ fails to have dense range.) In particular, and as an application, we obtain that such a space cannot support a topologically transitive operator.