A certain class of triangular algebras in type 𝐼𝐼₁ hyperfinite factors

Baker, Richard

doi:10.1090/S0002-9939-1991-1049840-3

A certain class of triangular algebras in type $\textrm {II}_ 1$ hyperfinite factors
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Proc. Amer. Math. Soc. 112 (1991), 163-169 Request permission

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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