TY - JOUR
T1 - Ergodic invariant states and irreducible representations of crossed product C*-algebras
AU - Huang, Huichi
AU - Wu, Jianchao
N1 - Publisher Copyright:
© Theta, 2017.
PY - 2017/6/1
Y1 - 2017/6/1
N2 - Motivated by reformulating Furstenberg's ×p,×q conjecture via representations of a crossed product C*-algebra, we show that in a discrete C*-dynamical system (A, Γ), the space of (ergodic) Γ-invariant states on A is homeomorphic to a subspace of (pure) state space of A ⋊ Γ. Various applications of this in topological dynamical systems and representation theory are obtained.
AB - Motivated by reformulating Furstenberg's ×p,×q conjecture via representations of a crossed product C*-algebra, we show that in a discrete C*-dynamical system (A, Γ), the space of (ergodic) Γ-invariant states on A is homeomorphic to a subspace of (pure) state space of A ⋊ Γ. Various applications of this in topological dynamical systems and representation theory are obtained.
UR - https://www.scopus.com/pages/publications/85022089936
UR - https://www.scopus.com/pages/publications/85022089936#tab=citedBy
U2 - 10.7900/jot.2016jun11.2141
DO - 10.7900/jot.2016jun11.2141
M3 - Article
AN - SCOPUS:85022089936
SN - 0379-4024
VL - 78
SP - 159
EP - 172
JO - Journal of Operator Theory
JF - Journal of Operator Theory
IS - 1
ER -