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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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$K_ 0$ of certain subdiagonal subalgebras of von Neumann algebras
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by Richard Baker PDF
Proc. Amer. Math. Soc. 116 (1992), 13-19 Request permission

Abstract:

We show that ${K_0}$ of any finite maximal subdiagonal subalgebra of a separably acting finite von Neumann algebra is isomorphic to ${K_0}$ of the diagonal of the subalgebra. It results that ${K_0}$ of any finite, $\sigma$-weakly closed, maximal triangular subalgebra of a separably acting finite von Neumann algebra is isomorphic to ${K_0}$ of the diagonal of the subalgebra, provided that the diagonal of the subalgebra is a Cartan subalgebra of the von Neumann algebra. In addition, given any separably acting type ${\text {II}_1}$ factor $\mathcal {M}$, we explicitly compute ${K_0}$ of those triangular subalgebras $\mathcal {T}$ of $\mathcal {M}$ that have the property that there exists a UHF subalgebra $\mathcal {A}$ of $\mathcal {M}$ and a standard triangular UHF algebra $\mathcal {S}$ in $\mathcal {A}$ such that $\mathcal {A}$ is $\sigma$-weakly dense in $\mathcal {M}$ and $\mathcal {T}$ is the $\sigma$-weak closure of $\mathcal {S}$.
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 116 (1992), 13-19
  • MSC: Primary 46L80; Secondary 19A49
  • DOI: https://doi.org/10.1090/S0002-9939-1992-1093591-7
  • MathSciNet review: 1093591