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K0 of certain subdiagonal subalgebras of Von Neumann algebras
Journal article   Open access   Peer reviewed

K0 of certain subdiagonal subalgebras of Von Neumann algebras

Richard Baker
Proceedings of the American Mathematical Society, Vol.116(1), pp.13-19
01/01/1992
DOI: 10.1090/S0002-9939-1992-1093591-7
url
https://doi.org/10.1090/S0002-9939-1992-1093591-7View
Published (Version of record) Open Access

Abstract

We show that K 0 {K_0} of any finite maximal subdiagonal subalgebra of a separably acting finite von Neumann algebra is isomorphic to K 0 {K_0} of the diagonal of the subalgebra. It results that K 0 {K_0} of any finite, σ \sigma -weakly closed, maximal triangular subalgebra of a separably acting finite von Neumann algebra is isomorphic to K 0 {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 II 1 {\text {II}_1} factor M \mathcal {M} , we explicitly compute K 0 {K_0} of those triangular subalgebras T \mathcal {T} of M \mathcal {M} that have the property that there exists a UHF subalgebra A \mathcal {A} of M \mathcal {M} and a standard triangular UHF algebra S \mathcal {S} in A \mathcal {A} such that A \mathcal {A} is σ \sigma -weakly dense in M \mathcal {M} and T \mathcal {T} is the σ \sigma -weak closure of S \mathcal {S} .

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