Kadec–Klee properties of some quasi-Banach function spaces

Kolwicz, Paweł

doi:10.1007/s11117-018-0555-8

Cited by 5 publications

(2 citation statements)

References 34 publications

(63 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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%

See 1 more Smart Citation

Geometric properties of F-normed Orlicz spaces

et al. 2018

Self Cite

View full text Add to dashboard Cite

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.

show abstract

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

Self Cite

View full text Add to dashboard Cite

show abstract

Monotonicities of quasi‐normed Calderón–Lozanovskiĭ spaces with applications to approximation problems

Foralewski,

Kolwicz

2024

Mathematische Nachrichten

View full text Add to dashboard Cite

We consider the geometric structure of quasi‐normed Calderón–Lozanovskiĭ spaces. First, we study relations between the quasi‐norm and the quasi‐modular “near zero” and “near one,” which are fundamental for the theory. With their help, we provide a precise description of the basic monotonicity properties. In comparison with the well‐known normed case, we develop a number of new techniques and methods, among which the conditions and play a crucial role. From our general results, we conclude the criteria for monotonicity properties in quasi‐normed Orlicz spaces, which are new even in this particular context. We consider both the function and the sequence case as well as we admit degenerated Orlicz functions, which provides us with a maximal class of spaces under consideration. We also discuss the applications of suitable properties to the best dominated approximation problems in quasi‐Banach lattices.

show abstract

Copies of $$l^{\infty }$$ in Quasi-normed Calderón–Lozanovskiĭ Spaces

Foralewski,

Hudzik,

Kolwicz

2024

Results Math

View full text Add to dashboard Cite

We consider order isomorphic and order linearly isometric copies of $$l^{\infty }$$ l ∞ in the quasi-normed Calderón–Lozanovskiĭ spaces $$E_{\varphi }$$ E φ . We present a number of theorems describing these copies in the natural language of suitable properties of the quasi-normed ideal space E and the non-decreasing Orlicz function $$\varphi $$ φ . In particular, we will characterize quasi-normed Orlicz–Lorentz spaces having order isomorphic and order linearly isometric copies of $$l^{\infty }$$ l ∞ . Our studies are conducted in a full possible generality due to the measure space and the Orlicz function.

show abstract

Kadec–Klee properties of some quasi-Banach function spaces

Cited by 5 publications

References 34 publications

Geometric properties of F-normed Orlicz spaces

Geometric properties of F-normed Orlicz spaces

Monotonicities of quasi‐normed Calderón–Lozanovskiĭ spaces with applications to approximation problems

Copies of $$l^{\infty }$$ in Quasi-normed Calderón–Lozanovskiĭ Spaces

Contact Info

Product

Resources

About