Journal article
K0 of certain subdiagonal subalgebras of Von Neumann algebras
Proceedings of the American Mathematical Society, Vol.116(1), pp.13-19
01/01/1992
DOI: 10.1090/S0002-9939-1992-1093591-7
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} .
Details
- Title: Subtitle
- K0 of certain subdiagonal subalgebras of Von Neumann algebras
- Creators
- Richard Baker
- Resource Type
- Journal article
- Publication Details
- Proceedings of the American Mathematical Society, Vol.116(1), pp.13-19
- DOI
- 10.1090/S0002-9939-1992-1093591-7
- ISSN
- 0002-9939
- eISSN
- 1088-6826
- Publisher
- American Mathematical Society
- Language
- English
- Date published
- 01/01/1992
- Academic Unit
- Mathematics
- Record Identifier
- 9984240767402771
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