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Proceedings of the American Mathematical Society

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



A certain class of triangular algebras in type $ {\rm II}\sb 1$ hyperfinite factors

Author: Richard Baker
Journal: Proc. Amer. Math. Soc. 112 (1991), 163-169
MSC: Primary 46L35; Secondary 47D25
MathSciNet review: 1049840
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Abstract: Let $ S$ be the standard triangular UHF algebra in a UHF algebra $ A$, where the rank of $ A$ is a strictly increasing sequence of positive integers. Let $ M$ be the type $ II_{1}$ hyperfinite factor defined as the weak closure of $ A$ in the tracial representation of $ A$. Define $ T$ to be the weak closure of $ S$ in this representation. Then $ T$ is a reflexive, maximal weakly closed triangular algebra in $ M$. Moreover, $ T$ is irreducible relative to $ M$. We exhibit a strongly closed sublattice $ L$ of $ \operatorname{lat} T$ such that $ T = \operatorname{alg} L$.

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Keywords: Triangular algebras, hyperfinite factors
Article copyright: © Copyright 1991 American Mathematical Society