scholarly journals Monotonicities in Orlicz Spaces Equipped with Mazur-Orlicz F-Norm

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Xinran Bai ◽  
Yunan Cui ◽  
Joanna Kończak
Keyword(s):  
Convex Function ◽  
Unit Sphere ◽  
Monotone Function ◽  
Orlicz Spaces ◽  
Sequence Spaces ◽  
Line Segments ◽  
Basic Properties ◽  
Orlicz Sequence Spaces

Some basic properties in Orlicz spaces and Orlicz sequence spaces that are generated by monotone function equipped with the Mazur-Orlicz F-norm are studied in this paper. We give some relationships between the modulus and the Mazur-Orlicz F-norm. We obtain an interesting result that the norm of an element in line segments is formed by two elements on the unit sphere less than or equal to 1 if and only if that the monotone function is a convex function. The criterion that Orlicz spaces and Orlicz sequence spaces that are generated by monotone function equipped with the Mazur-Orlicz F-norm are strictly monotone or lower locally uniform monotone is presented.

scholarly journals The Schur and (weak) Dunford-Pettis properties in Banach lattices

2002 ◽  
Vol 73 (2) ◽  
pp. 251-278 ◽  
Author(s):  
Anna Kamińska ◽  
Mieczysław Mastyło
Keyword(s):  
Orlicz Spaces ◽  
Sufficient Conditions ◽  
Complete Characterization ◽  
Sequence Spaces ◽  
Banach Lattices ◽  
Schur Property ◽  
Atomic Measure ◽  
Orlicz Sequence Spaces ◽  
Necessary And Sufficient

AbstractWe study the Schur and (weak) Dunford-Pettis properties in Banach lattices. We show that l1, c0 and l∞ are the only Banach symmetric sequence spaces with the weak Dunford-Pettis property. We also characterize a large class of Banach lattices without the (weak) Dunford-Pettis property. In MusielakOrlicz sequence spaces we give some necessary and sufficient conditions for the Schur property, extending the Yamamuro result. We also present a number of results on the Schur property in weighted Orlicz sequence spaces, and, in particular, we find a complete characterization of this property for weights belonging to class ∧. We also present examples of weighted Orlicz spaces with the Schur property which are not L1-spaces. Finally, as an application of the results in sequence spaces, we provide a description of the weak Dunford-Pettis and the positive Schur properties in Orlicz spaces over an infinite non-atomic measure space.

scholarly journals Packing Constant in Orlicz Sequence Spaces Equipped with the p-Amemiya Norm

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Xin He ◽  
Jijie Yu ◽  
Yunan Cui ◽  
Xin Huo
Keyword(s):  
Sequence Space ◽  
Geometric Characteristic ◽  
Orlicz Spaces ◽  
Sequence Spaces ◽  
Orlicz Sequence Space ◽  
Orlicz Sequence Spaces ◽  
Relevant Work ◽  
Amemiya Norm

The problem of packing spheres in Orlicz sequence spacelΦ,pequipped with the p-Amemiya norm is studied, and a geometric characteristic about the reflexivity oflΦ,pis obtained, which contains the relevant work aboutlp  (p>1)and classical Orlicz spaceslΦdiscussed by Rankin, Burlak, and Cleaver. Moreover the packing constant as well as Kottman constant in this kind of spaces is calculated.

Weakly compact sets in Orlicz sequence spaces

2021 ◽  
pp. 1-14
Author(s):  
Siyu Shi ◽  
Zhongrui Shi ◽  
Shujun Wu
Keyword(s):  
Sequence Spaces ◽  
Compact Sets ◽  
Weakly Compact ◽  
Orlicz Sequence Spaces ◽  
Weakly Compact Sets

scholarly journals Local rotundity structure of Cesàro–Orlicz sequence spaces

2008 ◽  
Vol 345 (1) ◽  
pp. 410-419 ◽  
Author(s):  
Paweł Foralewski ◽  
Henryk Hudzik ◽  
Alicja Szymaszkiewicz
Keyword(s):  
Sequence Spaces ◽  
Orlicz Sequence Spaces

λ-Properties of Orlicz sequence spaces

1994 ◽  
Vol 59 (3) ◽  
pp. 239-249 ◽  
Author(s):  
Shutao Chen ◽  
Huiying Sun
Keyword(s):  
Sequence Spaces ◽  
Orlicz Sequence Spaces

Orlicz Spaces Without Strongly Extreme Points and Without H-Points

1993 ◽  
Vol 36 (2) ◽  
pp. 173-177 ◽  
Author(s):  
Henryk Hudzik
Keyword(s):  
Extreme Point ◽  
Orlicz Space ◽  
Unit Sphere ◽  
Orlicz Function ◽  
Orlicz Spaces ◽  
Extreme Points ◽  
Luxemburg Norm ◽  
Nonatomic Measure

AbstractW. Kurc [5] has proved that in the unit sphere of Orlicz space LΦ(μ) generated by an Orlicz function Φ satisfying the suitable Δ2-condition and equipped with the Luxemburg norm every extreme point is strongly extreme. In this paper it is proved in the case of a nonatomic measure μ that the unit sphere of the Orlicz space LΦ(μ) generated by an Orlicz function Φ which does not satisfy the suitable Δ2-condition and equipped with the Luxemburg norm has no strongly extreme point and no H-point.

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