Geodesic
Dixmier Traces and Unitary Representations
Funkcionalʹnyj analiz i ego priloženiâ, Tome 35 (2001) no. 1, pp. 40-52 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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