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 .

**[1]**W. B. Arveson,*Analyticity in operator algebras*, Amer. J. Math.**89**(1967), 578-642. MR**0223899 (36:6946)****[2]**R. L. Baker,*A certain class of triangular algebras in type**hyperfinite factors*, Proc. Amer. Math. Soc.**112**(1991), 163-169. MR**1049840 (91h:46106)****[3]**J. Dixmier,*Von Neumann algebras*, North Holland, Amsterdam, New York, and Oxford, 1981. MR**641217 (83a:46004)****[4]**P. S. Muhly, K.-S. Saito, and B. Solel,*Coordinates for triangular operators algebras*, Ann. of Math. (2)**127**(1988), 245-278. MR**932297 (89h:46088)****[5]**F. J. Murray and J. von Neumann,*On rings of operators*. IV, Ann. of Math. (2)**44**(1943), 716-808. MR**0009096 (5:101a)****[6]**D. R. Pitts,*On the**groups of nest algebras*, preprint.**[7]**-,*Factorization problems for nests: factorization methods and characterizations of the universal factorization property*, J. Funct. Anal.**79**(1988), 57-90. MR**950084 (90a:46160)****[8]**J. R. Peters and B. H. Wagner,*Triangular*AF*algebras and nest subalgebras of*UHF*algebras*, preprint. MR**1191255 (94c:46116)****[9]**C. Qiu,*-theory of analytic crossed products*, Rocky Mountain J. Math. (to appear). MR**1201109 (94d:46069)****[10]**J. Tomiyama,*On the projections of norm one in the direct product operator algebras*, Tôhoku Math. J. (2)**11**(1959), 305-313. MR**0108739 (21:7453)**

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

Article copyright:
© Copyright 1992
American Mathematical Society