A certain class of triangular algebras in type ii 1 hyperfinite factors

Richard Baker

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

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A certain class of triangular algebras in type ii 1 hyperfinite factors

Journal article

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A certain class of triangular algebras in type ii 1 hyperfinite factors

Richard Baker

Proceedings of the American Mathematical Society, Vol.112(1), pp.163-169

1991

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

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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 II1, hyperfinite factor defined as the weak closure of A in the tracial representation of A. Define S to be the weak closure of S in this representation. Then J is a reflexive, maximal weakly closed triangular algebra in M. Moreover, J is irreducible relative to M. We exhibit a strongly closed sublattice ℒ of lat J such that J = algℒ.

Hyperfinite factors

Triangular algebras

Details

Title: Subtitle: A certain class of triangular algebras in type ii 1 hyperfinite factors
Creators: Richard Baker - University of Iowa, Mathematics
Resource Type: Journal article
Publication Details: Proceedings of the American Mathematical Society, Vol.112(1), pp.163-169
DOI: 10.1090/S0002-9939-1991-1049840-3
ISSN: 0002-9939
eISSN: 1088-6826
Publisher: American Mathematical Society
Language: English
Date published: 1991
Academic Unit: Mathematics
Record Identifier: 9983985843302771

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