scholarly journals (Non-)weakly mixing operators and hypercyclicity sets

2009 ◽  
Vol 59 (1) ◽  
pp. 1-35 ◽  
Author(s):  
Frédéric Bayart ◽  
Étienne Matheron
Keyword(s):  
Mixing Operators ◽  
Weakly Mixing

Weakly mixing operators

2009 ◽  
pp. 75-94
Author(s):  
Frederic Bayart ◽  
Etienne Matheron
Keyword(s):  
Mixing Operators ◽  
Weakly Mixing

scholarly journals Mixing operators and small subsets of the circle

2016 ◽  
Vol 2016 (715) ◽  
Author(s):  
Frédéric Bayart ◽  
Étienne Matheron
Keyword(s):  
Banach Spaces ◽  
Gaussian Measure ◽  
Linear Operators ◽  
Mixing Operators ◽  
Strongly Mixing ◽  
Weakly Mixing

AbstractWe provide complete characterizations, on Banach spaces with cotype 2, of those linear operators which happen to be weakly mixing or strongly mixing transformations with respect to some nondegenerate Gaussian measure. These characterizations involve two families of small subsets of the circle: the countable sets and the so-called

scholarly journals S-Mixing Tuple of Operators on Banach Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Wei Wang ◽  
Yonglu Shu ◽  
Xingzhong Wang
Keyword(s):  
Banach Spaces ◽  
Sufficient Condition ◽  
Mixing Operators ◽  
Weakly Mixing

We consider the question: what is the appropriate formulation of Godefroy-Shapiro criterion for tuples of operators? We also introduce a new notion about tuples of operators,S-mixing, which lies between mixing and weakly mixing. We also obtain a sufficient condition to ensure a tuple of operators to beS-mixing. Moreover, we study some new properties ofS-mixing operators on several concrete Banach spaces.

scholarly journals A topological lens for a measure-preserving system

2010 ◽  
Vol 31 (1) ◽  
pp. 49-75 ◽  
Author(s):  
E. GLASNER ◽  
M. LEMAŃCZYK ◽  
B. WEISS
Keyword(s):  
Topological Entropy ◽  
Periodic Points ◽  
Positive Entropy ◽  
Topological Properties ◽  
Topologically Transitive ◽  
Topological System ◽  
Zero Entropy ◽  
Weakly Mixing ◽  
Dynamical Properties

AbstractWe introduce a functor which associates to every measure-preserving system (X,ℬ,μ,T) a topological system $(C_2(\mu ),\tilde {T})$ defined on the space of twofold couplings of μ, called the topological lens of T. We show that often the topological lens ‘magnifies’ the basic measure dynamical properties of T in terms of the corresponding topological properties of $\tilde {T}$. Some of our main results are as follows: (i) T is weakly mixing if and only if $\tilde {T}$ is topologically transitive (if and only if it is topologically weakly mixing); (ii) T has zero entropy if and only if $\tilde {T}$ has zero topological entropy, and T has positive entropy if and only if $\tilde {T}$ has infinite topological entropy; (iii) for T a K-system, the topological lens is a P-system (i.e. it is topologically transitive and the set of periodic points is dense; such systems are also called chaotic in the sense of Devaney).

Mixing for stationary processes with finite-order multiple Wiener-Itô integral representation

1996 ◽  
Vol 16 (5) ◽  
pp. 1087-1100
Author(s):  
Eric Slud ◽  
Daniel Chambers
Keyword(s):  
Large Class ◽  
Order Term ◽  
Sufficient Conditions ◽  
Polynomial Form ◽  
Itô Integral ◽  
Ito Integral ◽  
Weakly Mixing ◽  
Subordinated Processes ◽  
Infinite Sums ◽  
Necessary And Sufficient

abstractNecessary and sufficient analytical conditions are given for homogeneous multiple Wiener-Itô integral processes (MWIs) to be mixing, and sufficient conditions are given for mixing of general square-integrable Gaussian-subordinated processes. It is shown that every finite or infinite sum Y of MWIs (i.e. every real square-integrable stationary polynomial form in the variables of an underlying weakly mixing Gaussian process) is mixing if the process defined separately by each homogeneous-order term is mixing, and that this condition is necessary for a large class of Gaussian-subordinated processes. Moreover, for homogeneous MWIs Y1, for sums of MWIs of order ≤ 3, and for a large class of square-integrable infinite sums Y1, of MWIs, mixing holds if and only if Y2 has correlation-function decaying to zero for large lags. Several examples of the criteria for mixing are given, including a second-order homogeneous MWI, i.e. a degree two polynomial form, orthogonal to all linear forms, which has auto-correlations tending to zero for large lags but is not mixing.

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