Dirichlet series and uniform ergodic theorems for linear operators in Banach spaces
Yoshimoto, Takeshi
Studia Mathematica, Tome 141 (2000), p. 69-83 / Harvested from The Polish Digital Mathematics Library
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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=μn of positive numbers and a sequence f=fn of functions analytic in neighborhoods of the spectrum σ(T), the Dirichlet series for fn(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.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:216774 
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Yoshimoto, Takeshi. Dirichlet series and uniform ergodic theorems for linear operators in Banach spaces. Studia Mathematica, Tome 141 (2000) pp. 69-83. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv141i1p69bwm/

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