The description of (commutative and noncommutative) $L_p$-isometries has been studied thoroughly since the seminal work of Banach. In the present paper, we provide a complete description for the limiting case, isometries on noncommutative $L_0$-spaces, which extends the Banach–Stone theorem and Kadison's theorem for isometries of von Neumann algebras. The result is new even in the commutative setting.

中文翻译：

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非交换 L0 空间的线性等距

（可交换和不可交换）的描述$L_p$-自从巴纳赫的开创性工作以来，等距学就得到了深入的研究。在本文中，我们提供了极限情况的完整描述，即非交换的等距$L_0$-空间，扩展了冯诺依曼代数等距的巴纳赫-斯通定理和卡迪森定理。即使在可交换的情况下，结果也是新的。