The entropy of rational Powers shifts

Author:
Geoffrey L. Price

Journal:
Proc. Amer. Math. Soc. **126** (1998), 1715-1720

MSC (1991):
Primary 46L55, 46L40, 46L10

DOI:
https://doi.org/10.1090/S0002-9939-98-04304-4

MathSciNet review:
1443405

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Abstract | References | Similar Articles | Additional Information

Abstract: The Connes-Størmer entropy of all rational Powers shifts is shown to be .

**[C]**M. Choda,*Entropy for -endomorphisms and relative entropy for subalgebras*, J. Operator Theory**25**(1991), 125-140. MR**94a:46098****[CNT]**A. Connes, H. Narnhofer and W. Thirring,*Dynamical entropy of -algebras and von Neumann algebras*, Commun. Math. Phys.**112**(1987), 691-719. MR**89b:46078****[CS]**A. Connes and E. Størmer,*Entropy for automorphisms of von Neumann algebras*, Acta Math.**134**(1975), 289-306. MR**56:12906****[GS]**V. Golodets and E. Størmer,*Entropy of -dynamical systems defined by bitstreams*, Univ. of Oslo preprint, 1996.**[NST]**H. Narnhofer, E. Størmer and W. Thirring,*A - dynamical system for which the tensor product formula for entropy fails*, Ergodic Theory and Dynamical Systems**15**(1995), 961-968. CMP**96:03****[NT]**H. Narnhofer and W. Thirring,*Chaotic properties of the non-commutative 2-shift*, From Phase Transitions to Chaos, World Science Publishing, 1992, pp. 530-546. MR**93i:46119****[Po]**R. T. Powers,*An index theory for semigroups of and type factors*, Canad. J. Math.**40**(1988), 86-114. MR**89f:46116****[PP1]**R. T. Powers and G. Price,*Binary shifts on the hyperfinite factor*, American Mathematical Society Series in Contemporary Mathematics**145**(1993), 453-464. MR**94h:46098****[PP2]**R. T. Powers and G. Price,*Cocycle conjugacy classes of shifts on the hyperfinite factor*, J. Funct. Anal.**121**(1994), 275-295. MR**95g:46110****[P1]**G. Price,*Shifts on the hyperfinite factor*, USNA preprint.**[P2]**G. Price,*Cocycle conjugacy classes of shifts on the hyperfinite factor*, J. Oper. Theory, to appear.**[P3]**G. Price,*Shifts on type factors*, Canad. J. Math.**39**(1987), 492-511. MR**88i:46080**

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Additional Information

**Geoffrey L. Price**

Affiliation:
Department of Mathematics 9E, United States Naval Academy, Annapolis, Maryland 21012

Email:
glp@sma.usna.navy.mil

DOI:
https://doi.org/10.1090/S0002-9939-98-04304-4

Keywords:
Entropy,
automorphisms,
endomorphisms,
factor,
von Neumann algebras,
noncommutative dynamical systems

Received by editor(s):
November 19, 1996

Additional Notes:
The author was supported in part by a grant from the National Security Agency and by a United States Naval Academy Recognition Grant

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1998
American Mathematical Society