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A note on cocycle-conjugate endomorphisms of von Neumann algebras

Author: Remus Floricel
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 2013-2018
MSC (2000): Primary 46L10, 46L40
Published electronically: January 7, 2004
MathSciNet review: 2053973
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Abstract: We show that two cocycle-conjugate endomorphisms of an arbitrary von Neumann algebra that satisfy certain stability conditions are conjugate endomorphisms, when restricted to some specific von Neumann subalgebras. As a consequence of this result, we obtain a new criterion for conjugacy of Powers shift endomorphisms acting on factors of type $\rm {I}_{\infty}.$

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  • [A] W. Arveson, Continuous analogues of Fock space, Mem. Amer. Math. Soc. 80 (1989), no. 409. MR 90f:47061
  • [BJP] O. Bratteli, P. Jorgensen, and G. Price, Endomorphisms of ${\mathcal B}({\mathcal H})$, Proc. Sympos. Pure Math. 59 (1996), 93-138. MR 97h:46107
  • [BY1] D. Bures and H. Yin, Shifts on the hyperfinite factor of type $\rm {II}\sb{1}$, J. Operator Theory 20 (1988), no. 1, 91-106. MR 90c:46082
  • [BY2] D. Bures and H. Yin, Outer conjugacy of shifts on the hyperfinite ${\rm II}\sb 1$-factor, Pacific J. Math. 142 (1990), no. 2, 245-257. MR 91k:46074
  • [Ch] M. Choda, Square roots of the canonical shifts, J. Operator Theory 31 (1994), no. 1, 145-163. MR 96b:46086
  • [Cu] J. Cuntz, Simple $C\sp*$-algebras generated by isometries, Comm. Math. Phys. 57 (1977), no. 2, 173-185. MR 57:7189
  • [L] M. Laca, Endomorphisms of ${\mathcal B}({\mathcal H})$ and Cuntz algebras, J. Operator Theory 30 (1993), no. 1, 85-108. MR 95m:46100
  • [P] R. Powers, An index theory for semigroups of $\sp *$-endomorphisms of ${\mathfrak{B}}({\mathfrak{H}})$ and type ${\rm II}\sb 1$ factors, Canad. J. Math. 40 (1988), no. 1, 86-114. MR 89f:46116
  • [Pr] G. Price, Shifts on the hyperfinite $\rm II\sb 1$ factor, J. Funct. Anal. 156 (1998), no. 1, 121-169. MR 99h:46118
  • [S] S. Stratila, Modular theory in operator algebras, Editura Academiei Republicii Socialiste Romania, Bucharest; Abacus Press, Tunbridge Wells, 1981. MR 85g:46072

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Additional Information

Remus Floricel
Affiliation: Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario, Canada, K1N 6N5

Keywords: von Neumann algebras, endomorphisms, cocycle-conjugacy, shifts
Received by editor(s): March 17, 2003
Published electronically: January 7, 2004
Communicated by: David R. Larson
Article copyright: © Copyright 2004 American Mathematical Society

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