Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

$ K\sb 0$ of certain subdiagonal subalgebras of von Neumann algebras


Author: Richard Baker
Journal: Proc. Amer. Math. Soc. 116 (1992), 13-19
MSC: Primary 46L80; Secondary 19A49
MathSciNet review: 1093591
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46L80, 19A49

Retrieve articles in all journals with MSC: 46L80, 19A49


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1093591-7
PII: S 0002-9939(1992)1093591-7
Article copyright: © Copyright 1992 American Mathematical Society