Kadison-Singer格的结构与强Kadison-Singer代数的构造

The structure of Kadison-Singer lattices and the construction of strong Kadison-Singer algebras

本文研究Kadison-Singer格的结构和强Kadison-Singer代数的构造,证明有限维Hilbert空间上的有限Kadison-Singer格不包含非平凡的约化投影,并且在无限维可分Hilbert空间的n重直和上构造了一类强Kadison-Singer代数.作为推论,本文给出了存在两个Kadison-Singer代数其斜积是一个强Kadison-Singer代数的例子.

In this paper,we study the structure of Kadison-Singer lattices and strong Kadison-Singer algebras.We prove that every finite Kadison-Singer lattice on a finite-dimensional Hilbert space has no nontrivial reducing projections and construct a class of strong Kadison-Singer algebras on n-fold direct sums of infinite-dimensional separable Hilbert spaces.As a corollary,we show that there exist two Kadison-Singer algebras,such that their skew product is a strong Kadison-Singer algebra.