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

DOI:
https://doi.org/10.1090/S0002-9939-1992-1093591-7

MathSciNet review:
1093591

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Abstract: We show that of any finite maximal subdiagonal subalgebra of a separably acting finite von Neumann algebra is isomorphic to of the diagonal of the subalgebra. It results that of any finite, -weakly closed, maximal triangular subalgebra of a separably acting finite von Neumann algebra is isomorphic to 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 factor , we explicitly compute of those triangular subalgebras of that have the property that there exists a UHF subalgebra of and a standard triangular UHF algebra in such that is -weakly dense in and is the -weak closure of .

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DOI:
https://doi.org/10.1090/S0002-9939-1992-1093591-7

Article copyright:
© Copyright 1992
American Mathematical Society