Geodesic
On a property of $L_p$ spaces on semifinite von Neumann algebras
Matematičeskie zametki, Tome 64 (1998) no. 2, pp. 185-190

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A characterization of the traces in a broad class of weights on von Neumann algebras is obtained. A new property of the “domain ideals” of these traces is proved. In the semifinite case, a relation for a faithful normal trace is established. This result is new even for the algebra of all bounded operators on a Hilbert space. Applications of the main result to the structure theory of von Neumann algebras and to the Köthe duality theory for ideal spaces of Segal measurable operators are given. 
@article{MZM_1998_64_2_a2,
     author = {A. M. Bikchentaev},
     title = {On a property of $L_p$ spaces on semifinite von {Neumann} algebras},
     journal = {Matemati\v{c}eskie zametki},
     pages = {185--190},
     publisher = {mathdoc},
     volume = {64},
     number = {2},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_2_a2/}
}
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A. M. Bikchentaev. On a property of $L_p$ spaces on semifinite von Neumann algebras. Matematičeskie zametki, Tome 64 (1998) no. 2, pp. 185-190. http://geodesic.mathdoc.fr/item/MZM_1998_64_2_a2/