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

Studia Mathematica (2000)

- Volume: 141, Issue: 1, page 69-83
- ISSN: 0039-3223

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topYoshimoto, Takeshi. "Dirichlet series and uniform ergodic theorems for linear operators in Banach spaces." Studia Mathematica 141.1 (2000): 69-83. <http://eudml.org/doc/216774>.

@article{Yoshimoto2000,

abstract = {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.},

author = {Yoshimoto, Takeshi},

journal = {Studia Mathematica},

keywords = {Abel method; uniform ergodicity; nilpotent operator; Dirichlet averages; power-boundedness},

language = {eng},

number = {1},

pages = {69-83},

title = {Dirichlet series and uniform ergodic theorems for linear operators in Banach spaces},

url = {http://eudml.org/doc/216774},

volume = {141},

year = {2000},

}

TY - JOUR

AU - Yoshimoto, Takeshi

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

JO - Studia Mathematica

PY - 2000

VL - 141

IS - 1

SP - 69

EP - 83

AB - 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.

LA - eng

KW - Abel method; uniform ergodicity; nilpotent operator; Dirichlet averages; power-boundedness

UR - http://eudml.org/doc/216774

ER -

## References

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- [8] M. Mbekhta et J. Zemánek, Sur le théorème ergodique uniforme et le spectre, C. R. Acad. Sci. Paris Sér. I Math. 317 (1993), 1155-1158.
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- [11] T. Yoshimoto, Uniform and strong ergodic theorems in Banach spaces, Illinois J. Math. 42 (1998), 525-543; Correction, ibid. 43 (1999), 800-801. Zbl0924.47005

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