scholarly journals Dilation equations and Markov operators

2005 ◽  
Vol 309 (1) ◽  
pp. 307-312 ◽  
Author(s):  
Janusz Morawiec
Keyword(s):  
Markov Operators ◽  
Dilation Equations

Factorization of an adjontable Markov operator

2019 ◽  
Vol 22 (02) ◽  
pp. 1950013
Author(s):  
Carlo Pandiscia
Keyword(s):  
Hilbert Space ◽  
Matrix Algebra ◽  
Unitary Operator ◽  
Markov Operator ◽  
Factorization Property ◽  
Markov Operators ◽  
Dilation Theory ◽  
Probability Spaces

In this work, we propose a method to investigate the factorization property of a adjontable Markov operator between two algebraic probability spaces without using the dilation theory. Assuming the existence of an anti-unitary operator on Hilbert space related to Stinespring representations of our Markov operator, which satisfy some particular modular relations, we prove that it admits a factorization. The method is tested on the two typologies of maps which we know admits a factorization, the Markov operators between commutative probability spaces and adjontable homomorphism. Subsequently, we apply these methods to particular adjontable Markov operator between matrix algebra which fixes the diagonal.

scholarly journals Weak Markov operators

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5453-5457
Author(s):  
Hūlya Duru ◽  
Serkan Ilter
Keyword(s):  
Positive Operator ◽  
Extreme Points ◽  
Markov Operator ◽  
Weak Order ◽  
Markov Operators

Let A and B be f -algebras with unit elements eA and eB respectively. A positive operator T from A to B satisfying T(eA) = eB is called a Markov operator. In this definition we replace unit elements with weak order units and, in this case, call T to be a weak Markov operator. In this paper, we characterize extreme points of the weak Markov operators.

The Poisson boundary of covering Markov operators

1995 ◽  
Vol 89 (1-3) ◽  
pp. 77-134 ◽  
Author(s):  
Vadim Kaimanovich
Keyword(s):  
Poisson Boundary ◽  
Markov Operators

Wavelets and differential-dilation equations

1996 ◽  
pp. 69-72
Author(s):  
T. Cooklev ◽  
G. Berbecel ◽  
A.N. Venetsanopoulos
Keyword(s):  
Dilation Equations

scholarly journals Lower bounds and the asymptotic behaviour of positive operator semigroups

2017 ◽  
Vol 38 (8) ◽  
pp. 3012-3041 ◽  
Author(s):  
MORITZ GERLACH ◽  
JOCHEN GLÜCK
Keyword(s):  
Lower Bound ◽  
Asymptotic Behaviour ◽  
Lower Bounds ◽  
Simple Proof ◽  
Continuous Operator ◽  
Banach Lattices ◽  
Operator Semigroups ◽  
Markov Operators ◽  
Discrete Semigroups ◽  
Analytical Tools

If $(T_{t})$ is a semigroup of Markov operators on an $L^{1}$-space that admits a non-trivial lower bound, then a well-known theorem of Lasota and Yorke asserts that the semigroup is strongly convergent as $t\rightarrow \infty$. In this article we generalize and improve this result in several respects. First, we give a new and very simple proof for the fact that the same conclusion also holds if the semigroup is merely assumed to be bounded instead of Markov. As a main result, we then prove a version of this theorem for semigroups which only admit certain individual lower bounds. Moreover, we generalize a theorem of Ding on semigroups of Frobenius–Perron operators. We also demonstrate how our results can be adapted to the setting of general Banach lattices and we give some counterexamples to show optimality of our results. Our methods combine some rather concrete estimates and approximation arguments with abstract functional analytical tools. One of these tools is a theorem which relates the convergence of a time-continuous operator semigroup to the convergence of embedded discrete semigroups.

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