# Journal of Operator Theory

Volume 74, Issue 2, Fall 2015 pp. 457-483.

Strongly continuous orbit equivalence of
one-sided topological Markov shifts

**Authors**:
Kengo Matsumoto

**Author institution:** Department of Mathematics,
Joetsu University of Education,
Joetsu, 943-8512, Japan

**Summary: ** We prove that
one-sided topological Markov shifts
$(X_A, \sigma_A)$
and
$(X_B, \sigma_B)$
are strongly continuous orbit equivalent
if and only if
there exists an isomorphism between
the Cuntz--Krieger algebras
${\mathcal{O}}_A$ and
${\mathcal{O}}_B$
preserving their maximal commutative $C^*$-subalgebras
$C(X_A)$ and $C(X_B)$
and giving cocycle conjugate gauge actions.
An example of one-sided topological
Markov shifts which are
strongly continuous orbit equivalent
but not one-sided topologically conjugate
is presented.

**DOI: **http://dx.doi.org/10.7900/jot.2014aug19.2063

**Keywords: ** Cuntz-Krieger algebras, gauge action,
topological Markov shifts, orbit equivalence

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