We show that positive surjective isometries between symmetric spaces associated with semi-finite von Neumann algebras are projection disjointness preserving if they are finiteness preserving. This is subsequently used to obtain a structural description of such isometries. Furthermore, it is shown that if the initial symmetric space is a strongly symmetric space with absolutely continuous norm, then a similar structural description can be obtained without requiring positivity of the isometry.

中文翻译：

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与半有限von Neumann代数相关的非交换对称空间之间的等价性

我们证明，与半有限冯·诺依曼代数相关的对称空间之间的正射影等距如果是有限性的，则是投影不相干性的。随后将其用于获得此类等距的结构描述。此外，示出了，如果初始对称空间是具有绝对连续范数的强对称空间，则无需等轴测图的正性就可以获得类似的结构描述。