标题： 遗传C*-子代数格 显示英文标题

标题： Hereditary C*-Subalgebra Lattices

摘要： 我们研究了遗传承C*-子代数格$\mathcal{H}(A)$与*-零化正交格$\mathscr{P}(A)^\perp$之间的联系。特别地，我们将$\mathcal{H}(A)$的$\vee$-分配元素表征为理想，回答了一个25年前的问题，使得$\mathcal{H}(A)$的量化结构能够完全由其格结构确定。我们还证明了$\mathscr{P}(A)^\perp$是分离的，从而允许进行与原始冯·诺伊曼代数类型分解完全一致的C*-代数类型分解。 显示英文摘要

摘要： We investigate the connections between order and algebra in the hereditary C*-subalgebra lattice $\mathcal{H}(A)$ and *-annihilator ortholattice $\mathscr{P}(A)^\perp$. In particular, we characterize $\vee$-distributive elements of $\mathcal{H}(A)$ as ideals, answering a 25 year old question, allowing the quantale structure of $\mathcal{H}(A)$ to be completely determined from its lattice structure. We also show that $\mathscr{P}(A)^\perp$ is separative, allowing for C*-algebra type decompositions which are completely consistent with the original von Neumann algebra type decompositions.