Abstract

We study the poset of partial isometries in \(C^{\ast}\)-algebras endowed with the \(\ast\)-order and \(\ast\)-orthogonality. We show that this structure is a complete Jordan invariant for \(AW^{\ast}\)-algebras. We prove that partial isometries in von Neumann algebras form a lower semilattice. The structures of partial isometries and projections are compared.

中文翻译：

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$$\boldsymbol{C}^{\mathbf{\ast}}$$ -Algebras 中的星序和部分等距

摘要

我们研究了\(C^{\ast}\) -代数中部分等距的偏序集，该代数具有\(\ast\) -阶和\(\ast\) -正交性。我们证明该结构是\(AW^{\ast}\) -代数的完整 Jordan 不变量。我们证明了冯诺依曼代数中的部分等距形成了一个下半格。比较了部分等距和投影的结构。