Dirichlet series and uniform ergodic theorems for linear operators in Banach spaces
Studia Mathematica, Tome 141 (2000) no. 1, pp. 69-83
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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^{-μ_nz} f_n(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.
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author = {Takeshi Yoshimoto},
title = {Dirichlet series and uniform ergodic theorems for linear operators in {Banach} spaces},
journal = {Studia Mathematica},
pages = {69--83},
publisher = {mathdoc},
volume = {141},
number = {1},
year = {2000},
doi = {10.4064/sm-141-1-69-83},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-141-1-69-83/}
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Takeshi Yoshimoto. Dirichlet series and uniform ergodic theorems for linear operators in Banach spaces. Studia Mathematica, Tome 141 (2000) no. 1, pp. 69-83. doi: 10.4064/sm-141-1-69-83
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