非交换 L0 空间的线性等距性

IF 0.8 3区数学 Q2 MATHEMATICS Bulletin of the London Mathematical Society Pub Date : 2024-04-12 DOI:10.1112/blms.13044

Aleksey Ber, Jinghao Huang, Fedor Sukochev

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摘要

自巴纳赫的开创性工作以来，人们对（交换和非交换）Lp$L_p$-等距的描述进行了深入研究。在本文中，我们对极限情况，即非交换 L0$L_0$ 空间上的等距进行了完整的描述，扩展了巴纳赫-斯通定理和卡迪森定理对冯-诺依曼代数方程等距的描述。这一结果即使在交换环境中也是全新的。

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Linear isometries of noncommutative L 0 $L_0$ -spaces

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.