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arXiv · 1301.5737

Normal states of type III factors

Yasuyuki Kawahigashi·Yoshiko Ogata·Erling Størmer
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Abstract

Let M be a factor of type III with separable predual and with normal states phi_1,...,phi_k, omega with omega faithful. Let A be a finite dimensional C*-subalgebra of M. Then it is shown that there is a unitary operator u in M such that phi_i Ad u =omega on A for i=1,...,k. This follows from an embedding result of a finite dimensional C*-algebra with a faithful state into M with finitely many given states. We also give similar embedding results of C*-algebras and von Neumann algebras with faithful states into M. Another similar result for a factor of type II_1 instead of type III holds.

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Yasuyuki Kawahigashi, Yoshiko Ogata, Erling Størmer. 2013-06-07. Normal states of type III factors. https://doi.org/10.2140/pjm.2014.267.131

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