Geometry and the Jones projection of a state |
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Authors: | Esteban Andruchow Alejandro Varela |
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Institution: | (1) Dpto. de Matemática, FCEyN Ciudad Universitaria, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina;(2) Dpto. de Economía y Matemática, Universidad de San Andres, Vito Dumas 284 esq. Arias, 1644 Victoria, Argentina |
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Abstract: | LetA be a von Neumann algebra and a faithful normal state. ThenO
= {
ºAd(g
1) :g G
A
}andU
= {
ºAd(u
*) :u U
A
are homogeneous reductive spaces. IfA is aC
* algebra,e
the Jones projection of the faithful state viewed as a conditional expectation, then we prove that the similarity orbit ofe
by invertible elements ofA can be imbedded inAA in such a way thate
is carried to 1 1 and the orbit ofe
to a homogeneous reductive space and an analytic submanifold ofAA. |
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Keywords: | 46L30 58B10 |
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