Weak Closure Theorem fails for ℤ²-actions

T. Downarowicz; J. Kwiatkowski

Displaying similar documents to “Weak Closure Theorem fails for ℤ²-actions”

Phenomena in rank-one ℤ²-actions

Tomasz Downarowicz, Jacek Serafin (2009)

Studia Mathematica

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We present an example of a rank-one partially mixing ℤ²-action which possesses a non-rigid factor and for which the Weak Closure Theorem fails. This is in sharp contrast to one-dimensional actions, which cannot display this type of behavior.

Mixing rank-one actions of locally compact abelian groups

Alexandre I. Danilenko, Cesar E. Silva (2007)

Annales de l'I.H.P. Probabilités et statistiques

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Weakly mixing rank-one transformations conjugate to their squares

Alexandre I. Danilenko (2008)

Studia Mathematica

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Utilizing the cut-and-stack techniques we construct explicitly a weakly mixing rigid rank-one transformation T which is conjugate to T². Moreover, it is proved that for each odd q, there is such a T commuting with a transformation of order q. For any n, we show the existence of a weakly mixing T conjugate to T² and whose rank is finite and greater than n.

Finite rank $ℤ^{d}$ actions and the loosely Bernoulli property.

Johnson, Aimee S.A., Şahin, Ayşe A. (1998)

The New York Journal of Mathematics [electronic only]

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Orbit equivalence rigidity.

Furman, Alex (1999)

Annals of Mathematics. Second Series

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Local rigidity of actions of higher rank abelian groups and KAM method.

Damjanović, Danijela, Katok, Anatole (2004)

Electronic Research Announcements of the American Mathematical Society [electronic only]

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Automatic continuity of biorthogonality preservers between weakly compact JB-triples and atomic JBW-triples

María Burgos, Jorge J. Garcés, Antonio M. Peralta (2011)

Studia Mathematica

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We prove that every biorthogonality preserving linear surjection from a weakly compact JB*-triple containing no infinite-dimensional rank-one summands onto another JB*-triple is automatically continuous. We also show that every biorthogonality preserving linear surjection between atomic JBW*-triples containing no infinite-dimensional rank-one summands is automatically continuous. Consequently, two atomic JBW*-triples containing no rank-one summands are isomorphic if and only if there...