Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Powers's binary shifts on the hyperfinite factor of type $ {\rm II}\sb 1$


Authors: Masatoshi Enomoto and Yasuo Watatani
Journal: Proc. Amer. Math. Soc. 105 (1989), 371-374
MSC: Primary 46L10; Secondary 46L35, 46L55
DOI: https://doi.org/10.1090/S0002-9939-1989-0938911-6
MathSciNet review: 938911
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A unit preserving $ *$-endomorphism $ \sigma $ on the hyperfinite $ {\text{I}}{{\text{I}}_1}$ factor $ R$ is called a shift if $ \bigcap\nolimits_{n = 0}^\infty {{\sigma ^n}(R) = \{ \lambda 1;\lambda \in \mathbb{C}} \} $. A shift $ \sigma $ is called Powers' binary shift if there is a self-adjoint unitary $ u$ such that $ R = \{ {\sigma ^n}(u);n \in \mathbb{N} \cup \{ 0\} \} ''$ and $ {\sigma ^k}(u)u = \pm u{\sigma ^k}(u)$ for $ k \in \mathbb{N} \cup \{ 0\} $. Let $ q(\sigma )$ be the number $ \min \{ k \in \mathbb{N};{\sigma ^k}(R)' \cap R \ne \mathbb{C}1\} $. It is shown that the number $ q(\sigma )$ is not the complete outer conjugacy invariant for Powers' binary shifts.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46L10, 46L35, 46L55

Retrieve articles in all journals with MSC: 46L10, 46L35, 46L55


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0938911-6
Keywords: Binary shifts, hyperfinite factor of type $ {\text{I}}{{\text{I}}_1}$, outer conjugacy invariant, relative commutant algebras
Article copyright: © Copyright 1989 American Mathematical Society