Quantales and C∗‐Algebras
Quantales and C∗‐Algebras
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DOI：
10.1112/jlms/s2-40.3.398
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发表时间：
1989-12
影响因子：
1.2
通讯作者：
F. Borceux;J. Rosický;G. Bossche
中科院分区：
文献类型：
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作者：
F. Borceux;J. Rosický;G. Bossche
交换C*-代数完全由它的闭理想格决定。Akemann[1，2]和Giles和Kummer[7]在任意单位C*-代数A的闭右理想格上发现了一种结构，使得类似于在交换情况下确定A成为可能。Mulvey[10]提出了一种使用闭右理想乘法的更代数的方法。我们正在进一步发展他的建议。在第一节中，我们很快地回忆起[3]中关于Quantales的一些基本定义和事实，并介绍一些新的定义和事实。在第二节中，我们讨论C*-代数的这些概念。我们的主要结果是，任何后素数C*-代数都是由它的闭右理想的乘法格决定的。
A commutative C*-algebra is known to be completely determined by its lattice of closed ideals. Akemann [1, 2] and Giles and Kummer [7] found a structure on the lattice of closed right ideals of an arbitrary unital C*-algebra A which makes it possible to determine A analogously as in the commutative case. Mulvey [10] has suggested a more algebraic approach using the multiplication of closed right ideals. We are further developing his suggestion. In Section 1, we quickly recall from [3] some basic definitions and facts about quantales and introduce some new ones. In Section 2 we discuss these notions for C*-algebras. Our main result is that any postliminary C*-algebra is determined by its multiplicative lattice of closed right ideals.