A certain class of triangular algebras in type 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 be the standard triangular UHF algebra in a UHF algebra , where the rank of is a strictly increasing sequence of positive integers. Let be the type hyperfinite factor defined as the weak closure of in the tracial representation of . Define to be the weak closure of in this representation. Then is a reflexive, maximal weakly closed triangular algebra in . Moreover, is irreducible relative to . We exhibit a strongly closed sublattice of such that .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1991-1049840-3

Keywords:
Triangular algebras,
hyperfinite factors

Article copyright:
© Copyright 1991
American Mathematical Society