Uniform convergence of stochastic semigroups. (English) Zbl 07533999
The authors do use the lattice structure and especially the notions of the quasi-interior point and the ideal generated by such a point in Lebasgue spaces, whose norm interior of the positive cone is empty, in order to study dynamical systems behaviour. Especially, the existence of quasi-interior points is associated to the erdodicity of such a dynamical system. A dynamical system is understood as a semigroup of integration operators acting on AL-Banach Lattices. Any element of such a semigroup maps any element of such a Banach Lattice to itself. The cardinality of these operators is equal to the continuum and the ergodidity is understoos as the behaviour of the ’mean’ operator. Such a mean operator is ergodic if it is a bounded operator. Since AL-norm’s properties are implied by the lattice structure of it, they are primarely assumed. The behaviour of such systems is associated to the implied differential operators’ semigroup.This is a pure contribution in theory and applications of infinitesemal operators in physics and economic science.
Reviewer: Christos E. Kountzakis (Karlovassi)
MSC:
| 47D06 | One-parameter semigroups and linear evolution equations |
| 47Bxx | Special classes of linear operators |
Citations:
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