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• # Artykuł - szczegóły

## Studia Mathematica

2001 | 147 | 2 | 131-153

## Differentiation of Banach-space-valued additive processes

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 < ∞.

131-153

wydano
2001

### Twórcy

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