mixing operators
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Author(s):  
Abhinav Chand ◽  
Leonel Robert ◽  
Arindam Sutradhar
Keyword(s):  

2020 ◽  
Vol 52 (3) ◽  
pp. 312-321
Author(s):  
Mansooreh Moosapoor

In this paper, we define subspace-ergodic operators and give examples of these operators. We show that by any given separable infinite-dimensional Banach space, subspace-ergodic operators can be constructed. We demonstrate that an invertible operator T is subspace-ergodic if and only if T-1 is subspace-ergodic. We prove that the direct sum of two subspace-ergodic operators is subspace-ergodic and if the direct sum of two operators is subspace-ergodic, then each of them is subspace-ergodic. Also, we investigate relations between subspace-ergodic and subspace-mixing operators. For example, we show that if T is subspace-mixing and invertible, then Tn and T-n are subspace-ergodic for n∈ℕ.


Author(s):  
H.-P. BEISE ◽  
L. FRERICK ◽  
J. MÜLLER

Abstract For arbitrary closed countable subsets Z of the unit circle examples of topologically mixing operators on Hilbert spaces are given which have a densely spanning set of eigenvectors with unimodular eigenvalues restricted to Z. In particular, these operators cannot be ergodic in the Gaussian sense.


2020 ◽  
Vol 6 (1) ◽  
pp. 127-142
Author(s):  
Abdelhamid Tallab

AbstractIn this paper, we introduce the notion of (q, p)-mixing operators from the injective tensor product space E ̂⊗∈F into a Banach space G which we call (q, p, F)-mixing. In particular, we extend the notion of (q, p, E)-summing operators which is a special case of (q, p, F)-mixing operators to Lipschitz case by studying their properties and showing some results for this notion.


2018 ◽  
pp. 903-931 ◽  
Author(s):  
D. Achour ◽  
E. Dahia ◽  
M. A. S. Saleh

2016 ◽  
Vol 8 (1) ◽  
pp. 3-10
Author(s):  
N. Bamerni ◽  
A. Kilicman

In this this paper, we introduce new classes of operators in complex Banach spaces, which we call $k$-bitransitive operators and compound operators to study the direct sum of diskcyclic operators. We create a set of sufficient conditions for an operator to be $k$-bitransitive or compound. We give a relation between topologically mixing operators and compound operators. Also, we extend the Godefroy-Shapiro Criterion for topologically mixing operators to compound operators.


Author(s):  
Frédéric Bayart ◽  
Étienne Matheron

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


2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Wei Wang ◽  
Yonglu Shu ◽  
Xingzhong Wang

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.


2014 ◽  
Vol 92 (12) ◽  
pp. 3038-3045 ◽  
Author(s):  
María del Carmen Sandate-Trejo ◽  
Arturo Jiménez-Gutiérrez ◽  
Mahmoud El-Halwagi

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