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
安广宇 1赵丹妮 1程星 1房甜1
作者信息
- 1. 陕西科技大学数学与数据科学学院,西安 710021
- 折叠
摘要
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.
Abstract
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.
关键词
Kadison-Singer格/强Kadison-Singer代数/约化投影Key words
Kadison-Singer lattice/strong Kadison-Singer algebra/reducing projection引用本文复制引用
基金项目
陕西省自然科学基础研究计划(2023-JC-YB-043)
出版年
2024
NETL
NSTL
万方数据