scholarly journals Strongly mixing operators on Hilbert spaces and speed of mixing

2013 ◽  
Vol 106 (6) ◽  
pp. 1394-1434
Author(s):  
Vincent Devinck
Keyword(s):  
Hilbert Spaces ◽  
Mixing Operators ◽  
Strongly 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

Mixing operators with prescribed unimodular eigenvalues

2020 ◽  
pp. 1-8
Author(s):  
H.-P. BEISE ◽  
L. FRERICK ◽  
J. MÜLLER
Keyword(s):  
Unit Circle ◽  
Hilbert Spaces ◽  
Mixing Operators ◽  
Spanning Set ◽  
Topologically Mixing

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.

Unbounded Linear Operators

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Von Neumann ◽  
Limit Circle ◽  
Sectorial Operators ◽  
Closed Operators ◽  
The Stability ◽  
Symmetric Operators ◽  
Unbounded Linear Operators ◽  
Special Case

This chapter is concerned with closable and closed operators in Hilbert spaces, especially with the special classes of symmetric, J-symmetric, accretive and sectorial operators. The Stone–von Neumann theory of extensions of symmetric operators is treated as a special case of results for compatible adjoint pairs of closed operators. Also discussed in detail is the stability of closedness and self-adjointness under perturbations. The abstract results are applied to operators defined by second-order differential expressions, and Sims’ generalization of the Weyl limit-point, limit-circle characterization for symmetric expressions to J-symmetric expressions is proved.

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