Kadec–Klee properties of some quasi-Banach function spaces

Kolwicz, Paweł

doi:10.1007/s11117-018-0555-8

Cited by 2 publications

(2 citation statements)

References 34 publications

(63 reference statements)

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“…Now, we are going to study the Kadec-Klee properties in Orlicz spaces equipped with the Mazur-Orlicz F-norm. Recall that these properties have already been investigated in some Banach and quasi-Banach lattices by many authors (see for instance, [5,8,11,12,19,21,[26][27][28]).…”

Section: N=1mentioning

confidence: 99%

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Geometric properties of F-normed Orlicz spaces

et al. 2018

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The paper deals with F-normed functions and sequence spaces. First, some general results on such spaces are presented. But most of the results in this paper concern various monotonicity properties and various Kadec-Klee properties of F-normed Orlicz functions and sequence spaces and their subspaces of elements with order continuous norm, when they are generated by monotone Orlicz functions on R + and equipped with the classical Mazur-Orlicz F-norm. Strict monotonicity, lower (and upper) local uniform monotonicity and uniform monotonicity in the classical sense as well as their orthogonal counterparts are considered. It follows from the criteria that are presented for these properties that all the above classical monotonicity properties except for uniform monotonicity differ from their orthogonal counterparts [in contrast to Köthe spaces (see Hudzik et al. in Rocky Mt J Math 30(3):933-950, 2000)]. The Kadec-Klee properties that are considered in this paper correspond to various kinds of convergence: convergence locally in measure and convergence globally in measure for function spaces, uniform convergence and coordinatewise convergence in the case of sequence spaces.

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Section: N=1mentioning

confidence: 99%

“…Our paper offers an extension of results on monotonicity and Kadec-Klee properties of Banach function lattices to F -normed function lattices, specifically to F -normed Orlicz spaces (compare with [5,[8][9][10][11][12]19,21,22,24,[26][27][28]33,34]).…”

Section: Introductionmentioning

confidence: 99%

Geometric properties of F-normed Orlicz spaces

et al. 2018

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On the Properties of Quasi-Banach Function Spaces

Nekvinda,

Peša

2024

J Geom Anal

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In this paper we explore some basic properties of quasi-Banach function spaces which are important in applications. Namely, we show that they possess a generalised version of Riesz–Fischer property, that embeddings between them are always continuous, and that the dilation operator is bounded on them. We also provide a characterisation of separability for quasi-Banach function spaces over the Euclidean space. Furthermore, we extend the classical Riesz–Fischer theorem to the context of quasinormed spaces and, as a consequence, obtain an alternative proof of completeness of quasi-Banach function spaces.

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Kadec–Klee properties of some quasi-Banach function spaces

Cited by 2 publications

References 34 publications

Geometric properties of F-normed Orlicz spaces

Geometric properties of F-normed Orlicz spaces

On the Properties of Quasi-Banach Function Spaces

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