Conjugacies between ergodic transformations and their inverses
Colloquium Mathematicum, Tome 84 (2000) no. 1, pp. 185-193
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
We study certain symmetries that arise when automorphisms S and T defined on a Lebesgue probability space (X, ℱ, μ) satisfy the equation $ST = T^{-1}S $. In an earlier paper [6] it was shown that this puts certain constraints on the spectrum of T. Here we show that it also forces constraints on the spectrum of $S^{2}$. In particular, $S^{2}$ has to have a multiplicity function which only takes even values on the orthogonal complement of the subspace ${ f ∈ L^{2}(X, ℱ, μ): f(T^{2}x) = f(x) }$. For S and T ergodic satisfying this equation further constraints arise, which we illustrate with examples. As an application of these results we give a general method for constructing weakly mixing rank one maps T for which $T^{2}$ has non-simple spectrum.
@article{10_4064_cm_84_85_1_185_193,
author = {Geoffrey Goodson},
title = {Conjugacies between ergodic transformations and their inverses},
journal = {Colloquium Mathematicum},
pages = {185--193},
year = {2000},
volume = {84},
number = {1},
doi = {10.4064/cm-84/85-1-185-193},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm-84/85-1-185-193/}
}
TY - JOUR AU - Geoffrey Goodson TI - Conjugacies between ergodic transformations and their inverses JO - Colloquium Mathematicum PY - 2000 SP - 185 EP - 193 VL - 84 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4064/cm-84/85-1-185-193/ DO - 10.4064/cm-84/85-1-185-193 LA - en ID - 10_4064_cm_84_85_1_185_193 ER -
Geoffrey Goodson. Conjugacies between ergodic transformations and their inverses. Colloquium Mathematicum, Tome 84 (2000) no. 1, pp. 185-193. doi: 10.4064/cm-84/85-1-185-193
Cité par Sources :