scholarly journals Dynamics of weighted translations generated by group actions

Filomat ◽  
2020 ◽  
Vol 34 (7) ◽  
pp. 2131-2139
Author(s):  
Chung-Chuan Chen ◽  
Seyyed Tabatabaie ◽  
Ali Mohammadi
Keyword(s):  
Group Actions ◽  
Locally Compact Groups ◽  
Necessary Condition ◽  
Compact Groups ◽  
Locally Compact ◽  
Measure Spaces ◽  
Operator Functions ◽  
Cosine Operator Functions ◽  
Dynamical Properties ◽  
Sufficient And Necessary Condition

In this paper, we consider actions of locally compact groups on measure spaces, and give a sufficient and necessary condition for weighted translations on such spaces to be chaotic. Moreover, some dynamical properties for certain cosine operator functions, generated by translations, are proved as well.

Disjoint topological transitivity for weighted translations generated by group actions

2021 ◽  
Vol 71 (5) ◽  
pp. 1229-1240
Author(s):  
Chung-Chuan Chen ◽  
Seyyed Mohammad Tabatabaie ◽  
Ali Mohammadi
Keyword(s):  
Group Actions ◽  
Group Element ◽  
Necessary Condition ◽  
Compact Groups ◽  
Topological Transitivity ◽  
Locally Compact ◽  
Topological Mixing ◽  
Quotient Spaces ◽  
Sufficient And Necessary Condition

Abstract In this note, we give a sufficient and necessary condition for weighted translations, generated by group actions, to be disjoint topologically transitive in terms of the weights, the group element and the measure. The characterization of disjoint topological mixing is obtained as well. Moreover, we apply the results to the quotient spaces of locally compact groups and hypergroups.

Recurrence of Cosine Operator Functions on Groups

2016 ◽  
Vol 59 (4) ◽  
pp. 693-704 ◽  
Author(s):  
Chung-Chuan Chen
Keyword(s):  
Operator Function ◽  
Locally Compact Group ◽  
Necessary Condition ◽  
Multiple Recurrence ◽  
Locally Compact ◽  
Cosine Operator Function ◽  
Cosine Operator ◽  
Operator Functions ◽  
Cosine Operator Functions ◽  
Sufficient And Necessary Condition

AbstractIn this note, we study the recurrence and topologically multiple recurrence of a sequence of operators on Banach spaces. In particular, we give a sufficient and necessary condition for a cosine operator function, induced by a sequence of operators on the Lebesgue space of a locally compact group, to be topologically multiply recurrent.

Chaos for Cosine Operator Functions Generated by Shifts

2014 ◽  
Vol 24 (09) ◽  
pp. 1450108 ◽  
Author(s):  
Chung-Chuan Chen
Keyword(s):  
Operator Function ◽  
Weighted Shift ◽  
Necessary Condition ◽  
Weighted Shifts ◽  
Cosine Operator Function ◽  
Cosine Operator ◽  
Operator Functions ◽  
Cosine Operator Functions ◽  
Sufficient And Necessary Condition

Let 1 ≤ p < ∞. We give the sufficient and necessary condition for cosine operator functions, generated by bilateral weighted shifts on ℓp(ℤ), to be chaotic. Moreover, such a cosine operator function is chaotic if, and only if, its weighted shift is chaotic.

scholarly journals Large-scale geometry of homeomorphism groups

2017 ◽  
Vol 38 (7) ◽  
pp. 2748-2779 ◽  
Author(s):  
KATHRYN MANN ◽  
CHRISTIAN ROSENDAL
Keyword(s):  
Compact Manifold ◽  
Large Scale ◽  
Group Actions ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Identity Component ◽  
Rich Family ◽  
Large Scale Geometry ◽  
Homeomorphism Groups

Let $M$ be a compact manifold. We show that the identity component $\operatorname{Homeo}_{0}(M)$ of the group of self-homeomorphisms of $M$ has a well-defined quasi-isometry type, and study its large-scale geometry. Through examples, we relate this large-scale geometry to both the topology of $M$ and the dynamics of group actions on $M$. This gives a rich family of examples of non-locally compact groups to which one can apply the large-scale methods developed in previous work of the second author.

scholarly journals A higher category approach to twisted actions on c* -algebras

2012 ◽  
Vol 56 (2) ◽  
pp. 387-426 ◽  
Author(s):  
Alcides Buss ◽  
Ralf Meyer ◽  
Chenchang Zhu
Keyword(s):  
Classical Group ◽  
Group Actions ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Equivariant Maps ◽  
C Algebras ◽  
Covariant Representations ◽  
Group Case ◽  
Morita Equivalent

AbstractC*-algebras form a 2-category with *-homomorphisms or correspondences as morphisms and unitary intertwiners as 2-morphisms. We use this structure to define weak actions of 2-categories, weakly equivariant maps between weak actions and modifications between weakly equivariant maps. In the group case, we identify the resulting notions with known ones, including Busby–Smith twisted actions and the equivalence of such actions, covariant representations and saturated Fell bundles. For 2-groups, weak actions combine twists in the sense of Green, and Busby and Smith.The Packer–Raeburn Stabilization Trick implies that all Busby–Smith twisted group actions of locally compact groups are Morita equivalent to classical group actions. We generalize this to actions of strict 2-groupoids.

On the Lp-conjecture for locally compact groups

2007 ◽  
Vol 89 (3) ◽  
pp. 237-242 ◽  
Author(s):  
F. Abtahi ◽  
R. Nasr-Isfahani ◽  
A. Rejali
Keyword(s):  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact

Ergodic actions of group extensions on von Neumann algebras

1989 ◽  
Vol 112 (1-2) ◽  
pp. 71-112
Author(s):  
Klaus Thomsen
Keyword(s):  
Fixed Point ◽  
Von Neumann Algebras ◽  
Locally Compact Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Von Neumann ◽  
Finite Dimensional ◽  
Fixed Point Algebra ◽  
Atomic Centre

SynopsisWe consider automorphic actions on von Neumann algebras of a locally compact group E given as a topological extension 0 → A → E → G → 0, where A is compact abelian and second countable. Motivated by the wish to describe and classify ergodic actions of E when G is finite, we classify (up to conjugacy) first the ergodic actions of locally compact groups on finite-dimensional factors and then compact abelian actions with the property that the fixed-point algebra is of type I with atomic centre. We then handle the case of ergodic actions of E with the property that the action is already ergodic when restricted to A, and then, as a generalisation, the case of (not necessarily ergodic) actions of E with the property that the restriction to A is an action with abelian atomic fixed-point algebra. Both these cases are handled for general locally compact-countable G. Finally, we combine the obtained results to classify the ergodic actions of E when G is finite, provided that either the extension is central and Hom (G, T) = 0, or G is abelian and either cyclic or of an order not divisible by a square.

Sign in / Sign up

Export Citation Format

Share Document