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Ergodic theorems for linear operators on \(C(X)\) with strict topology. (English) Zbl 0815.28015
Author’s abstract: “If \(X\) is a completely regular Hausdorff space and if \(C(X)\) is provided by a suitable locally convex topology \(\mathcal T\), then there is a 1-1 correspondence between the continuous linear operators on \((C(X),{\mathcal T})\) and the integral operators defined by kernels on \(X\times M_ \Theta(X)\), where \(\Theta\in \{t,\tau,\sigma\}\) according to the selection of \(\mathcal T\). This fact is used for study of certain asymptotic properties of solutions of evolution equations and for comparison of the statistical ergodic theorem with more recent results”.
Reviewer: L.Stoyanov (Perth)
MSC:
28D99 Measure-theoretic ergodic theory
47A35 Ergodic theory of linear operators
54H20 Topological dynamics (MSC2010)
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