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.