Abstract:
We show that for any C*-algebra A, a sufficiently large Hilbert space H and a unit vector ξ ∈ H, the natural application rep , π〈 π(-)ξ,ξ〉 is a topological quotient, where rep(A:H) is the space of representations on H and Q(A) the set of quasi-states, i.e. positive linear functionals with norm at most 1. This quotient might be a useful tool in the representation theory of C*-algebras. We apply it to give an interesting proof of Takesaki-Bichteler duality for C*-algebras which allows to drop a hypothesis.
Registro:
Documento: |
Artículo
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Título: | The quasi-state space of a C*-algebra is a topological quotient of the representation space |
Autor: | Yuhjtman, S.A. |
Filiación: | Universidad de Buenos Aires, FCEN, Departamento de Matemática, Ciudad Universitaria, Intendente Güiraldes 2160, Pabellón I, Ciudad Autónoma de Buenos Aires, C1428EGA, Argentina
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Año: | 2015
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Volumen: | 56
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Número: | 2
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Página de inicio: | 57
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Página de fin: | 65
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Título revista: | Revista de la Union Matematica Argentina
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Título revista abreviado: | Rev. Union Mat. Argent.
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ISSN: | 00416932
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00416932_v56_n2_p57_Yuhjtman |
Referencias:
- Bichteler, K., A generalization to the non-separable case of Takesaki's duality theorem for C*-algebras (1969) Invent. Math, 9, pp. 89-98. , MR 0253060
- Fujimoto, I., A Gelfand-Naimark theorem for C*-algebras (1998) Pacific J. Math, 184, pp. 95-119. , MR 1626504
- Takesaki, M., A duality in the representation theory of C*-algebras (1967) Ann. of Math. (2), 85, pp. 370-382. , MR 0209859
- Yuhjtman, S.A., (2013) Duality theorems for C*-algebras, multiplier algebra in duality contexts, Tietze extension theorem and related results, , http://digital.bl.fcen.uba.ar/gsdl-282/cgi-bin/library.cgi?a=d&c=tesis&d=Tesis_5365_Yuhjtman, Ph.D. thesis, Universidad de Buenos Aires
Citas:
---------- APA ----------
(2015)
. The quasi-state space of a C*-algebra is a topological quotient of the representation space. Revista de la Union Matematica Argentina, 56(2), 57-65.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00416932_v56_n2_p57_Yuhjtman [ ]
---------- CHICAGO ----------
Yuhjtman, S.A.
"The quasi-state space of a C*-algebra is a topological quotient of the representation space"
. Revista de la Union Matematica Argentina 56, no. 2
(2015) : 57-65.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00416932_v56_n2_p57_Yuhjtman [ ]
---------- MLA ----------
Yuhjtman, S.A.
"The quasi-state space of a C*-algebra is a topological quotient of the representation space"
. Revista de la Union Matematica Argentina, vol. 56, no. 2, 2015, pp. 57-65.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00416932_v56_n2_p57_Yuhjtman [ ]
---------- VANCOUVER ----------
Yuhjtman, S.A. The quasi-state space of a C*-algebra is a topological quotient of the representation space. Rev. Union Mat. Argent. 2015;56(2):57-65.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00416932_v56_n2_p57_Yuhjtman [ ]