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Displaying similar documents to “Extreme points of the Besicovitch--Orlicz space of almost periodic functions equipped with the Luxemburg norm”

Further properties of Stepanov--Orlicz almost periodic functions

Yousra Djabri, Fazia Bedouhene, Fatiha Boulahia (2020)

Commentationes Mathematicae Universitatis Carolinae

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We revisit the concept of Stepanov--Orlicz almost periodic functions introduced by Hillmann in terms of Bochner transform. Some structural properties of these functions are investigated. A particular attention is paid to the Nemytskii operator between spaces of Stepanov--Orlicz almost periodic functions. Finally, we establish an existence and uniqueness result of Bohr almost periodic mild solution to a class of semilinear evolution equations with Stepanov--Orlicz almost periodic forcing...

On extreme points of Orlicz spaces with Orlicz norm.

Henryk Hudzik, Marek Wisla (1993)

Collectanea Mathematica

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In the paper we consider a class of Orlicz spaces equipped with the Orlicz norm over a non-negative, complete and sigma-finite measure space (T,Sigma,mu), which covers, among others, Orlicz spaces isomorphic to L-infinite and the interpolation space L1 + L-infinite. We give some necessary conditions for a point x from the unit sphere to be extreme. Applying this characterization, in the case of an atomless measure mu, we find a description of the set of extreme points of L1 + L-infinite...

A strongly extreme point need not be a denting point in Orlicz spaces equipped with the Orlicz norm

Adam Bohonos, Ryszard Płuciennik (2011)

Banach Center Publications

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There are necessary conditions for a point x from the unit sphere to be a denting point of the unit ball of Orlicz spaces equipped with the Orlicz norm generated by arbitrary Orlicz functions. In contrast to results in [12, 17, 16], we present also examples of Orlicz spaces in which strongly extreme points of the unit ball are not denting points.

Roughness of two norms on Musielak-Orlicz function spaces

Jimin Zheng, Lihuan Sun, Yun'an Cui (2008)

Banach Center Publications

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In this paper, the criteria of strong roughness, roughness and pointwise roughness of Orlicz norm and Luxemburg norm on Musielak-Orlicz function spaces are obtained.

On property (β) of Rolewicz in Musielak-Orlicz sequence spaces equipped with the Orlicz norm

Paweł Kolwicz (2005)

Banach Center Publications

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We prove that the Musielak-Orlicz sequence space with the Orlicz norm has property (β) iff it is reflexive. It is a generalization and essential extension of the respective results from [3] and [5]. Moreover, taking an arbitrary Musielak-Orlicz function instead of an N-function we develop new methods and techniques of proof and we consider a wider class of spaces than in [3] and [5].