| Abstract: |
| It is well-known that the transition probabilities $P(x,A)$ of Markov processes naturally define a linear operator by $ Tf(x)=\\int f(y)P(x,dy)$, which is called {\\it Markov operator} and acts on $L^1$-spaces. The study of the entire process can be reduced to the study of the
limit behavior of the corresponding Markov operator. When we look at quantum analogous of Markov processes, it naturally appear in various directions of quantum physics. In these studies it is important to elaborate with associated quantum dynamical systems which eventually converge to a set of stationary states. From the mathematical point of view, ergodic properties of quantum Markov operators were investigated by many authors.
Since the study of several properties of physical and probabilistic processes in abstract framework is convenient and important, some applications of this scheme in
quantum information have been discussed We emphasize that the classical and quantum cases confine to this scheme. We point out that in this abstract scheme one considers a based normed spaces and mappings of these spaces. In this talk, in this setting certain ergodic properties of Markov operators are considered and investigated.Also the question about the sensitivity of stationary states and perturbations of the Markov chain are explored well. |
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