Geodesic
Dixmier Traces and Unitary Representations
Funkcionalʹnyj analiz i ego priloženiâ, Tome 35 (2001) no. 1, pp. 40-52.

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

As is known, for any two given unitary representations of a topological group in Hilbert spaces, a new unitary representation in the corresponding space of Hilbert–Schmidt mappings can be defined. In the paper, a modification of this construction is suggested that uses the Dixmier trace (instead of the ordinary operator trace). The case of the group of second-order real unimodular matrices is studied in detail. 
@article{FAA_2001_35_1_a3,
     author = {R. S. Ismagilov},
     title = {Dixmier {Traces} and {Unitary} {Representations}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {40--52},
     publisher = {mathdoc},
     volume = {35},
     number = {1},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2001_35_1_a3/}
}
TY  - JOUR
AU  - R. S. Ismagilov
TI  - Dixmier Traces and Unitary Representations
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2001
SP  - 40
EP  - 52
VL  - 35
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2001_35_1_a3/
LA  - ru
ID  - FAA_2001_35_1_a3
ER  - 
%0 Journal Article
%A R. S. Ismagilov
%T Dixmier Traces and Unitary Representations
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2001
%P 40-52
%V 35
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2001_35_1_a3/
%G ru
%F FAA_2001_35_1_a3
R. S. Ismagilov. Dixmier Traces and Unitary Representations. Funkcionalʹnyj analiz i ego priloženiâ, Tome 35 (2001) no. 1, pp. 40-52. http://geodesic.mathdoc.fr/item/FAA_2001_35_1_a3/

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

[2] Shubin M. A., Psevdodifferentsialnye operatory i spektralnaya teoriya, Nauka, M., 1978 | MR

[3] Gokhberg I. Ts., Krein M. G., Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov, Nauka, M., 1965

[4] Trudy seminara N. Burbaki za 1989 g, Mir, M., 1991 | MR

[5] Connes A., Noncommutative Geometry, Academic Press, 1994 | MR | Zbl