Geometry and the Jones projection of a state
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: | , |
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1996
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| 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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| Sumario: | 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. |
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