Classically Normal Pure States |
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| Authors: | Charles Akemann Nik Weaver |
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| Institution: | (1) Department of Mathematics, University of California, Santa Barbara, CA 93106, USA;(2) Department of Mathematics, Washington University in Saint Louis, Saint Louis, MO 63130, USA |
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| Abstract: | A pure state f of a von Neumann algebra
is called classically normal if f is normal on any von Neumann subalgebra of
on which f is multiplicative. Assuming the continuum hypothesis, a separably represented von Neumann algebra M has classically normal, singular pure states iff there is a central projection p ∈M such that pMp is a factor of type I∞, II, or III. |
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| Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 46L10 |
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