A class of shifts on the hyperfinite factor

Authors:
Donald Bures and Hong Sheng Yin

Journal:
Proc. Amer. Math. Soc. **110** (1990), 169-175

MSC:
Primary 46L35

DOI:
https://doi.org/10.1090/S0002-9939-1990-1013966-X

MathSciNet review:
1013966

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Abstract: We construct and classify up to conjugacy certain shifts on the hyperfinite -factor, each being a shift of Jones index which fails to be an -shift. In particular for each prime we construct uncountably many such shifts.

**[1]**A. Brown and P. R. Halmos,*Algebraic properties of Toeplitz operators*, J. Reine Angew. Math.**213**(1964), 89-102. MR**0160136 (28:3350)****[2]**D. Bures and H.-S. Yin,*Shifts on the hyperfinite factor of type*, J. Operator Theory**20**(1988), 91-106. MR**972183 (90c:46082)****[3]**-,*Outer conjugacy of shifts on the hyperfinite**-factor*, Pacific J. Math.**141**(1990).**[4]**M. Choda,*Shifts on the hyperfinite**-factor*, J. Operator Theory**17**(1987), 223-235. MR**887220 (88g:46075)****[5]**M. Choda, M. Enomoto, and Y. Watatani,*Uncountably many non-binary shifts on the hyperfinite**-factor*, preprint.**[6]**M. Enomoto and Y. Watatani,*A solution of Powers' problem on outer conjugacy of binary shifts*, preprint.**[7]**V. F. R. Jones,*Index for subfactors*, Invent. Math.**72**(1983), 1-25. MR**696688 (84d:46097)****[8]**R. T. Powers,*An index theory for semigroups of**-endomorphisms of**and type**-factors*, Canad. J. Math.**40**(1988), 86-114. MR**928215 (89f:46116)****[9]**G. Price,*Shifts on type**-factors*, Canad. J. Math.**39**(1987), 492-511. MR**899846 (88i:46080)****[10]**-,*Shifts of integer index on the hyperfinite**-factor*, Pacific J. Math.**132**(1988), 379-390. MR**934178 (89c:46088)**

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DOI:
https://doi.org/10.1090/S0002-9939-1990-1013966-X

Article copyright:
© Copyright 1990
American Mathematical Society