ORLICZ-LORENTZ SEQUENCE SPACES EQUIPPED WITH THE ORLICZ NORM In memory of Henryk Hudzik,a great man,our teacher and colleague  

作　　者：Yunan CUI Pawel FORALEWSKI Joanna KONCZAK 崔云安;Pawel FORALEWSKI;Joanna KONCZAK(Department of Mathematics,Harbin University of Science and Technology,Harbin 150080,China;Faculty of Mathematics and Computer Science,Adam Mickiewicz University,Poznan,Uniwersytetu Poznanshiego 4,61-614 Poznan,Poland)

机构地区：[1]Department of Mathematics,Harbin University of Science and Technology,Harbin 150080,China [2]Faculty of Mathematics and Computer Science,Adam Mickiewicz University,Poznan,Uniwersytetu Poznanshiego 4,61-614 Poznan,Poland

出　　处：《Acta Mathematica Scientia》2022年第2期623-652,共30页数学物理学报（B辑英文版）

基　　金：the supportof NSF of China(11871181)。

摘　　要：In this article,we consider Orlicz-Lorentz sequence spaces equipped with the Orlicz norm(λ_(φ,ω),‖·‖_(φ,ω)^(O))generated by any Orlicz function and any non-increasing weight sequence.As far as we know,research on such a general case is conducted for the first time.After showing that the Orlicz norm is equal to the Amemiya norm in general and giving some important properties of this norm,we study the problem of existence of order isomorphically isometric copies of l∞in the space(λ_(φ,ω),‖·‖_(φ,ω)^(O))and we find criteria for order continuity and monotonicity properties of this space.We also find criteria for monotonicity properties of n-dimensional subspaces λ_(φ,ω)^(n)(n≥2)and the subspace(λ_(φ,ω))_(a) of order continuous elements of λ_(φ,ω).Finally,as an immediate consequence of the criteria considered in this article,the properties of Orlicz sequence spaces equipped with the Orlicz norm are deduced.

关 键 词：Orlicz-Lorentz spaces Banach symmetric spaces Orlicz norm order continuity and copies of l^(∞) monotonicity properties 

分 类 号：O177[理学—数学]