全矩阵代数中的酉轨道
Unitary orbits in a full matrix algebra
摘要：
由正可逆（单位化）的Hilbert-Schmidt算子构成的Hilbert流形$Σ$具有丰富的结构和几何。酉轨道$Ω\subset Σ$的几何研究从拓扑和度量的观点：我们寻求的条件，确保存在一个光滑的局部结构的集合$Ω$，我们研究了凸性这一套的测地线结构时，我们给$Σ$两个黎曼度量。
英文摘要：
The Hilbert manifold $Σ$ consisting of positive invertible (unitized) Hilbert-Schmidt operators has a rich structure and geometry. The geometry of unitary orbits $Ω\subset Σ$ is studied from the topological and metric viewpoints: we seek for conditions that ensure the existence of a smooth local structure for the set $Ω$, and we study the convexity of this set for the geodesic structures that arise when we give $Σ$ two Riemannian metrics.
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