Displaying similar documents to “Quasi-compactness and uniform ergodicity of Markov operators”

On the uniform ergodic theorem in Banach spaces that do not contain duals

Vladimir Fonf, Michael Lin, Alexander Rubinov (1996)

Studia Mathematica

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Let T be a power-bounded linear operator in a real Banach space X. We study the equality (*) ( I - T ) X = z ∈ X : s u p n ∥ ∑ k = 0 n T k z ∥ < ∞ . For X separable, we show that if T satisfies and is not uniformly ergodic, then ( I - T ) X ¯ contains an isomorphic copy of an infinite-dimensional dual Banach space. Consequently, if X is separable and does not contain isomorphic copies of infinite-dimensional dual Banach spaces, then (*) is equivalent to uniform ergodicity. As an application, sufficient conditions for uniform ergodicity of irreducible...

Dirichlet series and uniform ergodic theorems for linear operators in Banach spaces

Takeshi Yoshimoto (2000)

Studia Mathematica

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We study the convergence properties of Dirichlet series for a bounded linear operator T in a Banach space X. For an increasing sequence μ = μ n of positive numbers and a sequence f = f n of functions analytic in neighborhoods of the spectrum σ(T), the Dirichlet series for f n ( T ) is defined by D[f,μ;z](T) = ∑n=0∞ e-μnz fn(T), z∈ ℂ. Moreover, we introduce a family of summation methods called Dirichlet methods and study the ergodic properties of Dirichlet averages for T in the uniform operator topology. ...