Nuclear faces of state spaces of $C^{\ast }$-algebras
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- by C. J. K. Batty PDF
- Proc. Amer. Math. Soc. 86 (1982), 275-278 Request permission
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 ${A_1}{ \otimes _\beta }{A_2}$.References
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Additional Information
- © Copyright 1982 American Mathematical Society
- 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