On quantales that classify C*-algebras ∗
On quantales that classify C*-algebras ∗
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发表时间：
2004-03
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通讯作者：
David Kruml;P. Resende
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作者：
David Kruml;P. Resende
Mulvey的函子Max赋值给每个单位C*-代数A一个A的闭线性子空间的单位对合量子Max A，并指出它对单位C*-代数进行到*-同构的分类。在本文中,我们提供了一个强大的事实的证明,每一个同构u:马克斯→Max B的unital involutive量子有∗同构B: a→B,马克斯B u恰逢当局限于左元素的马克斯·a。但我们也表明isomorphisms u:马克斯→Max B可能存在同构的v: a→B是马克斯v = u。
The functor Max of Mulvey assigns to each unital C*-algebra A the unital involutive quantale Max A of closed linear subspaces of A, and it has been remarked that it classifies unital C*-algebras up to ∗-isomorphism. In this paper we provide a proof of this and of the stronger fact that for every isomorphism u : Max A → Max B of unital involutive quantales there is a ∗-isomorphism b : A → B such that Max b u coincides with u when restricted to the left-sided elements of Max A. But we also show that isomorphisms u : Max A → Max B may exist for which no isomorphism v : A → B is such that Max v = u.