Geometry and the Jones projection of a state

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Let A be a von Neumann algebra and π a faithful normal state. Then Oπ = {π o Ad(g-1) : g ∈ GA} and Uπ = {π o Ad(u*) : u ∈ UA} are homogeneous reductive spaces. If A is a C* algebra, eπ the Jones projection of the faithful state π viewed as a conditional expectation, then we prove that the similarity...

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Autores principales: Andruchow, Esteban, Varela, Alejandro
Publicado: 1996
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0378620X_v25_n2_px_Andruchow
http://hdl.handle.net/20.500.12110/paper_0378620X_v25_n2_px_Andruchow
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_0378620X_v25_n2_px_Andruchow2023-06-08T15:40:25Z Geometry and the Jones projection of a state Andruchow, Esteban Varela, Alejandro Let A be a von Neumann algebra and π a faithful normal state. Then Oπ = {π o Ad(g-1) : g ∈ GA} and Uπ = {π o Ad(u*) : u ∈ UA} are homogeneous reductive spaces. If A is a C* algebra, eπ the Jones projection of the faithful state π viewed as a conditional expectation, then we prove that the similarity orbit of eπ by invertible elements of A can be imbedded in A ⊗ A in such a way that eπ is carried to 1 ⊗ 1 and the orbit of eπ to a homogeneous reductive space and an analytic submanifold of A ⊗ A. Fil:Andruchow, E. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Varela, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 1996 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0378620X_v25_n2_px_Andruchow http://hdl.handle.net/20.500.12110/paper_0378620X_v25_n2_px_Andruchow
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description Let A be a von Neumann algebra and π a faithful normal state. Then Oπ = {π o Ad(g-1) : g ∈ GA} and Uπ = {π o Ad(u*) : u ∈ UA} are homogeneous reductive spaces. If A is a C* algebra, eπ the Jones projection of the faithful state π viewed as a conditional expectation, then we prove that the similarity orbit of eπ by invertible elements of A can be imbedded in A ⊗ A in such a way that eπ is carried to 1 ⊗ 1 and the orbit of eπ to a homogeneous reductive space and an analytic submanifold of A ⊗ A.
author Andruchow, Esteban
Varela, Alejandro
spellingShingle Andruchow, Esteban
Varela, Alejandro
Geometry and the Jones projection of a state
author_facet Andruchow, Esteban
Varela, Alejandro
author_sort Andruchow, Esteban
title Geometry and the Jones projection of a state
title_short Geometry and the Jones projection of a state
title_full Geometry and the Jones projection of a state
title_fullStr Geometry and the Jones projection of a state
title_full_unstemmed Geometry and the Jones projection of a state
title_sort geometry and the jones projection of a state
publishDate 1996
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0378620X_v25_n2_px_Andruchow
http://hdl.handle.net/20.500.12110/paper_0378620X_v25_n2_px_Andruchow
work_keys_str_mv AT andruchowesteban geometryandthejonesprojectionofastate
AT varelaalejandro geometryandthejonesprojectionofastate
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