P无穷C* 代数中正规算子的闭酉轨道与相似轨道
Closed Unitary and Similarity Orbits of Normal Operators in Purely Infinite C*-Algebras
摘要：
我们将研究有单位的、简单的、纯无限C* 代数中正规算子的酉轨道和相似轨道的范数闭包。在平凡K_1-群代数中，给出了两个正规算子近似酉等价的分类的算子论证明。基于这些方法，得到了酉轨道间距离的上、下界。此外，对于有单位元的、简单的、纯无限的C* 代数和具有可分预对偶的III型因子，给出了一个正规算子在另一正规算子的闭相似轨道中的完整刻画.
英文摘要：
We will investigate the norm closure of the unitary and similarity orbits of normal operators in unital, simple, purely infinite C*-algebras. An operator theoretic proof will be given to the classification of when two normal operators are approximately unitarily equivalent in said algebras with trivial K_1-group. Some upper and lower bounds for the distance between unitary orbits will be obtained based on these methods. In addition, a complete characterization of when one normal operator is in the closed similarity orbit of another normal operator will be given for unital, simple, purely infinite C*-algebras and type III factors with separable predual.
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