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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