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Duality theory of vector-valued function spaces III

100%

Nowak M.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

1998

tom [Z] 38

101-108

The paper is a continuation of [5] and [6], where the duality theory of Banach-space valued function spaces E(X) is developed. We deal with order continuous linear functionals and singular linear functionals on E(X). We show that if (E,||ˇ||E) is a Banach function space then the singular dual E(X)~s is equal to the topological dual of E(X) provided with the Minkowski functional P of the set W = {f

On the sequential strong-weak closedness of the Nemytskij multivalued operator

100%

Nguyêñ H. T.

Demonstratio Mathematica

2002

tom Vol. 35, nr 2

367-374

H-points in Köthe-Bochner spaces

100%

Krassowska D.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

1999

tom [Z] 39

97-108

In the paper we prove that if a measure space is atom-free then under some conditions every H-point of the unit ball of the Köthe-Bochner space must be an extreme point of this ball. This gives a local version of a result of Casting and Płuciennik and generalizes a result of Hu and Lin.

The Young measure representation for weak cluster points of sequences in M-spaces of measurable functions

88%

Nguyen H. T. , Pączka D.

Bulletin of the Polish Academy of Sciences. Mathematics

2008

tom Vol. 56, no 2

109-120

Let (X, Y) be a duality pair of M-spaces X, Y of measurable functions from Ω ⊂ R[sup]n into R[sup]d. The paper deals with Y-weak cluster points φ of the sequence φ(•, z[sub]j(•)) in X, where z[sub]j: Ω→ R[sup]m is measurable for j ∈ N and φ: Ω x R[sup]m → R[sup]d is a Carathéodory function. We obtain general sufficient conditions, under which, for some negligible set Aφ, the integral I(φ,νx) := ∫R φ(x,λ) dνx(λ) exists for χ ∈ Ω \ Aφ and φ(x) = I(φ, νx) on Ω \ Aφ, where ν = {νx}x∈Ω is a measurable-dependent family of Radon probability measures on R[sup]m.

Bochner representable operators on Köthe-Bochner spaces

75%

Nowak M.

Commentationes Mathematicae

2008

tom Vol. 48, [Z] 2

113-119

Let E be a Banach function space and X be a real Banach space. We study Bochner representable operators from a K¨othe-Bochner space E(X) to a Banach space Y . We consider the problem of compactness and weak compactness of Bochner representable operators from E(X) (provided with the natural mixed topology) to Y .

On Property β of Rolewicz in Köthe–Bochner Function Spaces

63%

Kolwicz P.

Bulletin of the Polish Academy of Sciences. Mathematics

2005

tom Vol. 53, no 1

75-85

It is proved that the Köthe–Bochner function space E(X) has property β if and only if X is uniformly convex and E has property β. In particular, property β does not lift from X to E(X) in contrast to the case of Köthe–Bochner sequence spaces.