Differentiation of Banach-space-valued additive processes

• Autorzy: Ryotaro Sato
• Języki publikacji: EN

Abstrakty

EN

Let X be a Banach space and (Ω,Σ,μ) be a σ-finite measure space. Let L be a Banach space of X-valued strongly measurable functions on (Ω,Σ,μ). We consider a strongly continuous d-dimensional semigroup $T = {T(u): u = (u₁,...,u_{d})$, $u_{i} > 0$, 1 ≤ i ≤ d} of linear contractions on L. We assume that each T(u) has, in a sense, a contraction majorant and that the strong limit $T(0) = strong-lim_{u→0} T(u)$ exists. Then we prove, under some suitable norm conditions on the Banach space L, that a differentiation theorem holds for d-dimensional bounded processes in L which are additive with respect to the semigroup T. This generalizes a differentiation theorem obtained previously by the author under the assumption that L is an X-valued $L_{p}$-space, with 1 ≤ p < ∞.

Kategorie tematyczne

• 46E40: Spaces of vector- and operator-valued functions
• 47A35: Ergodic theory
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 47D03: Groups and semigroups of linear operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2001
• Tom: 147
• Numer: 2
• Strony: 131-153

Daty

wydano

2001

Twórcy

autor

Ryotaro Sato

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

Identyfikatory

DOI

10.4064/sm147-2-3