Henryk Hudzik
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View article: Copies of $$l^{\infty }$$ in Quasi-normed Calderón–Lozanovskiĭ Spaces
Copies of $$l^{\infty }$$ in Quasi-normed Calderón–Lozanovskiĭ Spaces Open
We consider order isomorphic and order linearly isometric copies of $$l^{\infty }$$ in the quasi-normed Calderón–Lozanovskiĭ spaces $$E_{\varphi }$$ . We present a number of theorems describing these copies in the natural language …
View article: Quasinormed spaces generated by a quasimodular
Quasinormed spaces generated by a quasimodular Open
In this paper, we introduce the notion of a quasimodular and we prove that the respective Minkowski functional of the unit quasimodular ball becomes a quasinorm. In this way, we refer to and complete the well-known theory related to the no…
View article: Quasi-modular spaces with applications to quasi-normed Calderón-Lozanovski\uı spaces
Quasi-modular spaces with applications to quasi-normed Calderón-Lozanovski\uı spaces Open
In this paper we introduce the notion of a quasi-modular and we prove that the respective Minkowski functional of the unit quasi-modular ball becomes a quasi-norm. In this way, we refer to and complete the well-known theory related to the …
View article: Kadec–Klee properties of Orlicz–Lorentz sequence spaces equipped with the Orlicz norm
Kadec–Klee properties of Orlicz–Lorentz sequence spaces equipped with the Orlicz norm Open
The necessary and sufficient conditions for both the Kadec–Klee property as well as the Kadec–Klee property with respect to the coordinatewise convergence in Orlicz–Lorentz sequence spaces equipped with the Orlicz norm and generated by arb…
View article: Surjectivity, Closed Range, and Fredholmness of the Composition and Multiplication Operators Between Possibly Distinct Orlicz Spaces
Surjectivity, Closed Range, and Fredholmness of the Composition and Multiplication Operators Between Possibly Distinct Orlicz Spaces Open
We give criteria for the closely related concepts of surjectivity, closed range, and Fredholmness of the composition and multiplication operators between possibly different Orlicz spaces over non-atomic measure spaces.
View article: Problems of existence of order copies of $$\ell ^\infty $$ ℓ ∞ and $$L_p(\nu )$$ L p ( ν ) in some non-Banach Köthe spaces
Problems of existence of order copies of $$\ell ^\infty $$ ℓ ∞ and $$L_p(\nu )$$ L p ( ν ) in some non-Banach Köthe spaces Open
For a monotone Orlicz function $$\varPhi $$ taking only values 0 and $$\infty $$ , it is showed that in both cases, the s-homogeneous norm $$\Vert \cdot \Vert _{\varPhi ,s}$$ , if $$\varPhi $$ is s-convex $$(00$$ as well as an order linear…
View article: Geometric properties of F-normed Orlicz spaces
Geometric properties of F-normed Orlicz spaces Open
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-nor…
View article: Geometry of Orlicz spaces equipped with norms generated by some lattice norms in $\mathbb{R}^{2}$
Geometry of Orlicz spaces equipped with norms generated by some lattice norms in $\mathbb{R}^{2}$ Open
In Orlicz spaces generated by convex Orlicz functions a family of norms generated by some lattice norms in $\mathbb{R}^{2}$ are defined and studied. This family of norms includes the family of the p-Amemiya norms ($1\leq p\leq\infty$) stud…
View article: M-constants in Orlicz-Lorentz sequence spaces with applications to fixed point theory
M-constants in Orlicz-Lorentz sequence spaces with applications to fixed point theory Open
In this paper some estimates of M -constants in Orlicz-Lorentz sequence spaces for both, the Luxemburg and the Amemiya norms are given.Since degenerated Orlicz functions ϕ and degenerated weighted sequences ω are also admitted, this invest…
View article: Basic properties of multiplication and composition operators between distinct Orlicz spaces
Basic properties of multiplication and composition operators between distinct Orlicz spaces Open
First, we present some simple (and easily verifiable) necessary conditions and sufficient conditions for boundedness of the multiplication operator $$M_u$$ and composition operator $$C_T$$ acting from Orlicz space $$L^{\Phi _1}(\Omega )$$ …
View article: Composition and multiplication operators between Orlicz function spaces
Composition and multiplication operators between Orlicz function spaces Open
Composition operators and multiplication operators between two Orlicz function spaces are investigated. First, necessary and sufficient conditions for their continuity are presented in several forms. It is shown that, in general, the Radon…