TY - JOUR
T1 - Quasi-factors of zero entropy systems
AU - Glasner, Eli
AU - Weiss, Benjamin
PY - 1995/7
Y1 - 1995/7
N2 - For minimal systems (X, T) of zero topological entropy we demonstrate the sharp difference between the behavior, regarding entropy, of the systems (M(X), T) and (2X, T) induced by T on the spaces M(X) of probability measures on X and 2X of closed subsets of X. It is shown that the system (M(X), T) has itself zero topological entropy. Two proofs of this theorem are given. The first uses ergodic theoretic ideas. The second relies on the different behavior of the Banach spaces (Equation presented) and (Equation presented) with respect to the existence of almost Hilbertian central sections of the unit ball. In contrast to this theorem we construct a minimal system (X, T) of zero entropy with a minimal subsystem (Y, T) of (2X, T) whose entropy is positive.
AB - For minimal systems (X, T) of zero topological entropy we demonstrate the sharp difference between the behavior, regarding entropy, of the systems (M(X), T) and (2X, T) induced by T on the spaces M(X) of probability measures on X and 2X of closed subsets of X. It is shown that the system (M(X), T) has itself zero topological entropy. Two proofs of this theorem are given. The first uses ergodic theoretic ideas. The second relies on the different behavior of the Banach spaces (Equation presented) and (Equation presented) with respect to the existence of almost Hilbertian central sections of the unit ball. In contrast to this theorem we construct a minimal system (X, T) of zero entropy with a minimal subsystem (Y, T) of (2X, T) whose entropy is positive.
UR - http://www.scopus.com/inward/record.url?scp=84967782933&partnerID=8YFLogxK
U2 - 10.1090/S0894-0347-1995-1270579-5
DO - 10.1090/S0894-0347-1995-1270579-5
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AN - SCOPUS:84967782933
SN - 0894-0347
VL - 8
SP - 665
EP - 686
JO - Journal of the American Mathematical Society
JF - Journal of the American Mathematical Society
IS - 3
ER -