Geodesic
Isometries on noncommutative symmetric spaces
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 496 (2021), pp. 64-67

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Let $\mathscr{M}$ be an atomless semifinite von Neumann algebra equipped with a faithful normal semifinite trace $\tau$ (or else, an atomic von Neumann algebra with all atoms having the same trace) acting on a separable Hilbert space $\mathscr{H}$. Let $E(\mathscr{M},\tau)$ be a separable symmetric space of $\tau$-measurable operators, whose norm is not proportional to the Hilbert norm $\|\cdot\|_2$ on $L_2(\mathscr{M},\tau)$. We provide a description of all bounded Hermitian operators on $E(\mathscr{M},\tau)$ and all surjective linear isometries of this space.
Keywords: surjective isometries, Hermitian operators, semifinite von Neumann algebra, symmetric spaces. 
@article{DANMA_2021_496_a13,
     author = {F. A. Sukochev and Jinghao Huang},
     title = {Isometries on noncommutative symmetric spaces},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {64--67},
     publisher = {mathdoc},
     volume = {496},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_496_a13/}
}
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F. A. Sukochev; Jinghao Huang. Isometries on noncommutative symmetric spaces. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 496 (2021), pp. 64-67. http://geodesic.mathdoc.fr/item/DANMA_2021_496_a13/