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

• Autorzy: Takeshi Yoshimoto
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2000
• Tom: 141
• Numer: 1
• Strony: 69-83

Daty

wydano

2000

otrzymano

1999-07-08

poprawiono

2000-03-31

Twórcy

autor

Takeshi Yoshimoto

• Department of Mathematics, Toyo University, Kawagoe, Saitama 350-8585 Japan

Bibliografia

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