Geodesic
On a property of $L_p$ spaces on semifinite von Neumann algebras
Matematičeskie zametki, Tome 64 (1998) no. 2, pp. 185-190 
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/
@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},
     year = {1998},
     volume = {64},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_2_a2/}
}
TY  - JOUR
AU  - A. M. Bikchentaev
TI  - On a property of $L_p$ spaces on semifinite von Neumann algebras
JO  - Matematičeskie zametki
PY  - 1998
SP  - 185
EP  - 190
VL  - 64
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MZM_1998_64_2_a2/
LA  - ru
ID  - MZM_1998_64_2_a2
ER  - 
%0 Journal Article
%A A. M. Bikchentaev
%T On a property of $L_p$ spaces on semifinite von Neumann algebras
%J Matematičeskie zametki
%D 1998
%P 185-190
%V 64
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_1998_64_2_a2/
%G ru
%F MZM_1998_64_2_a2

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Upmeier H., “Automorphism groups of Jordan $C^*$-algebras”, Math. Z., 176 (1981), 21–34 | DOI | MR | Zbl

[2] Ayupov Sh. A., Klassifikatsiya i predstavlenie uporyadochennykh iordanovykh algebr, FAN, Tashkent, 1986

[3] Takesaki M., Theory of operator algebras, I, Springer, New York–Heidelberg–Berlin, 1979

[4] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki, Funktsionalnyi analiz, Mir, M., 1977

[5] Dixmier J., “Existence de traces non normales”, C. R. Acad. Sci. Paris. Sér. A, 262 (1966), 1107–1108 | MR | Zbl

[6] Yeadon F. J., “Non-commutative $L_p$-spaces”, Math. Proc. Cambridge Philos. Soc., 77 (1975), 91–102 | DOI | MR | Zbl

[7] Dodds P. G., Dodds T. K.-Y., de Pagter B., “Noncommutative Köthe duality”, Trans. Amer. Math. Soc., 339 (1993), 717–750 | DOI | MR | Zbl

[8] Stroh A., West Graeme P., “$\tau$-compact operators affiliated to a semifinite von Neumann algebra”, Proc. Roy. Irish Acad. Sect. A, 93 (1993), 73–86 | MR

[9] Brown L. G., Kosaki H., “Jensen's inequality in semi-finite von Neumann algebras”, J. Operator Theory, 23 (1990), 3–19 | MR | Zbl

[10] Sherstnev A. N., “On certain problems in the theory of unbounded measures on projections”, Atti Sem. Mat. Fis. Univ. Modena, 42 (1994), 357–366 | MR | Zbl