The quasi-state space of a C*-algebra is a topological quotient of the representation space
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 mo...
Guardado en:
| Autor principal: | |
|---|---|
| Publicado: |
2015
|
| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00416932_v56_n2_p57_Yuhjtman http://hdl.handle.net/20.500.12110/paper_00416932_v56_n2_p57_Yuhjtman |
| Aporte de: |
| id |
paper:paper_00416932_v56_n2_p57_Yuhjtman |
|---|---|
| record_format |
dspace |
| spelling |
paper:paper_00416932_v56_n2_p57_Yuhjtman2023-06-08T15:04:48Z The quasi-state space of a C*-algebra is a topological quotient of the representation space Yuhjtman, Sergio A. 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. Fil:Yuhjtman, S.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2015 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00416932_v56_n2_p57_Yuhjtman http://hdl.handle.net/20.500.12110/paper_00416932_v56_n2_p57_Yuhjtman |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
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. |
| author |
Yuhjtman, Sergio A. |
| spellingShingle |
Yuhjtman, Sergio A. The quasi-state space of a C*-algebra is a topological quotient of the representation space |
| author_facet |
Yuhjtman, Sergio A. |
| author_sort |
Yuhjtman, Sergio A. |
| title |
The quasi-state space of a C*-algebra is a topological quotient of the representation space |
| title_short |
The quasi-state space of a C*-algebra is a topological quotient of the representation space |
| title_full |
The quasi-state space of a C*-algebra is a topological quotient of the representation space |
| title_fullStr |
The quasi-state space of a C*-algebra is a topological quotient of the representation space |
| title_full_unstemmed |
The quasi-state space of a C*-algebra is a topological quotient of the representation space |
| title_sort |
quasi-state space of a c*-algebra is a topological quotient of the representation space |
| publishDate |
2015 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00416932_v56_n2_p57_Yuhjtman http://hdl.handle.net/20.500.12110/paper_00416932_v56_n2_p57_Yuhjtman |
| work_keys_str_mv |
AT yuhjtmansergioa thequasistatespaceofacalgebraisatopologicalquotientoftherepresentationspace AT yuhjtmansergioa quasistatespaceofacalgebraisatopologicalquotientoftherepresentationspace |
| _version_ |
1768542827890868224 |