Vector-valued ergodic theorems for multiparameter additive processes

• Autorzy: Ryotaro Sato
• Języki publikacji: EN

Abstrakty

EN

Let X be a reflexive Banach space and (Ω,Σ,μ) be a σ-finite measure space. Let d ≥ 1 be an integer and T={T(u):u=($u_{1}$, ... ,$u_{d})$, $u_{i}$ ≥ 0, 1 ≤ i ≤ d } be a strongly measurable d-parameter semigroup of linear contractions on $L_{1}$((Ω,Σ,μ);X). We assume that to each T(u) there corresponds a positive linear contraction P(u) defined on $L_{1}$((Ω,Σ,μ);ℝ) with the property that ∥ T(u)f(ω)∥ ≤ P(u)∥f(·)∥(ω) almost everywhere on Ω for all f ∈ $L_{1}$((Ω,Σ,μ);X). We then prove stochastic and pointwise ergodic theorems for a d-parameter bounded additive process F in $L_{1}$((Ω,Σ,μ);X) with respect to the semigroup T.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1999
• Tom: 79
• Numer: 2
• Strony: 193-202

Daty

wydano

1999

otrzymano

1998-03-23

poprawiono

1998-06-26

Twórcy

autor

Ryotaro Sato

• Department of Mathematics Faculty of Science Okayama University Okayama, 700-8530 Japan

Bibliografia

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