Displaying similar documents to “Differentiation of Banach-space-valued additive processes”

On Simons' version of Hahn-Banach-Lagrange theorem

Jerzy Grzybowski, Hubert Przybycień, Ryszard Urbański (2014)

Banach Center Publications

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In this paper we generalize in Theorem 12 some version of Hahn-Banach Theorem which was obtained by Simons. We also present short proofs of Mazur and Mazur-Orlicz Theorem (Theorems 2 and 3).

Vector-valued ergodic theorems for multiparameter Additive processes II

Ryotaro Sato (2003)

Colloquium Mathematicae

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Previously we obtained stochastic and pointwise ergodic theorems for a continuous d-parameter additive process F in L₁((Ω,Σ,μ);X), where X is a reflexive Banach space, under the condition that F is bounded. In this paper we improve the previous results by considering the weaker condition that the function W ( · ) = e s s s u p | | F ( I ) ( · ) | | : I ⊂ [ 0 , 1 ) d is integrable on Ω.

Rademacher series from Orlicz to the present day

N. J. Kalton (2004)

Banach Center Publications

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We survey some questions on Rademacher series in both Banach and quasi-Banach spaces which have been the subject of extensive research from the time of Orlicz to the present day.

A semigroup analogue of the Fonf-Lin-Wojtaszczyk ergodic characterization of reflexive Banach spaces with a basis

Delio Mugnolo (2004)

Studia Mathematica

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In analogy to a recent result by V. Fonf, M. Lin, and P. Wojtaszczyk, we prove the following characterizations of a Banach space X with a basis. (i) X is finite-dimensional if and only if every bounded, uniformly continuous, mean ergodic semigroup on X is uniformly mean ergodic. (ii) X is reflexive if and only if every bounded strongly continuous semigroup is mean ergodic if and only if every bounded uniformly continuous semigroup on X is mean ergodic. ...

The Banach-Saks property in rearrangement invariant spaces

P. G. Dodds, E. M. Semenov, F. A. Sukochev (2004)

Studia Mathematica

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This paper studies the Banach-Saks property in rearrangement invariant spaces on the positive half-line. A principal result of the paper shows that a separable rearrangement invariant space E with the Fatou property has the Banach-Saks property if and only if E has the Banach-Saks property for disjointly supported sequences. We show further that for Orlicz and Lorentz spaces, the Banach-Saks property is equivalent to separability although the separable parts of some Marcinkiewicz spaces...

Mazur-Orlicz equality

Fon-Che Liu (2008)

Studia Mathematica

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A remarkable theorem of Mazur and Orlicz which generalizes the Hahn-Banach theorem is here put in a convenient form through an equality which will be referred to as the Mazur-Orlicz equality. Applications of the Mazur-Orlicz equality to lower barycenters for means, separation principles, Lax-Milgram lemma in reflexive Banach spaces, and monotone variational inequalities are provided.

Banach-Saks property in some Banach sequence spaces

Yunan Cui, Henryk Hudzik, Ryszard Płuciennik (1997)

Annales Polonici Mathematici

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It is proved that for any Banach space X property (β) defined by Rolewicz in [22] implies that both X and X* have the Banach-Saks property. Moreover, in Musielak-Orlicz sequence spaces, criteria for the Banach-Saks property, the near uniform convexity, the uniform Kadec-Klee property and property (H) are given.

Vector-valued ergodic theorems for multiparameter additive processes

Ryotaro Sato (1999)

Colloquium Mathematicae

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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...