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Proceedings of the American Mathematical Society

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Nuclear faces of state spaces of $ C\sp{\ast} $-algebras


Author: C. J. K. Batty
Journal: Proc. Amer. Math. Soc. 86 (1982), 275-278
MSC: Primary 46L05
DOI: https://doi.org/10.1090/S0002-9939-1982-0667288-2
MathSciNet review: 667288
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Abstract: Let $ {B_1}$ and $ {B_2}$ be maximal abelian subalgebras of $ {C^* }$-algebras $ {A_1}$ and $ {A_2}$, and suppose that for each pure state $ {\psi _1}$ of $ {B_1}$, the von Neumann algebra $ {p_{{\psi _1}}}A_1^{**}{p_{{\psi _1}}}$ is injective, where $ {p_{{\psi _1}}}$ is the common support in $ A_1^{**}$ of all the states of $ {A_1}$ which extend $ {\psi _1}$. Then $ {B_1} \otimes {B_2}$ is a maximal abelian subalgebra of any $ {C^*}$-tensor product $ {A_1}{ \otimes _\beta }{A_2}$.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0667288-2
Keywords: $ {C^* }$-tensor product, maximal abelian subalgebra, injective, nuclear
Article copyright: © Copyright 1982 American Mathematical Society

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