Normal structure of Lorentz-Orlicz spaces

Pei-Kee Lin; Huiying Sun

ArticleOriginal scientific text

Title

Normal structure of Lorentz-Orlicz spaces

Authors ¹, ²

Affiliations

Department of Mathematics, University of Memphis, Memphis, Tennessee 38152, U.S.A.
Department of Mathematics, Harbin Institute of Technology, Harbin, China

Abstract

Let ϕ: ℝ → ℝ₊ ∪ {0} be an even convex continuous function with ϕ(0) = 0 and ϕ(u) > 0 for all u > 0 and let w be a weight function. u₀ and v₀ are defined by u₀ = sup{u: ϕ is linear on (0,u)}, v₀=sup{v: w is constant on (0,v)} (where sup∅ = 0). We prove the following theorem. Theorem. Suppose that

Λ_{ϕ, w} (0, \infty)

(respectively,

Λ_{ϕ, w} (0, 1)

) is an order continuous Lorentz-Orlicz space. (1)

Λ_{ϕ, w}

has normal structure if and only if u₀ = 0 (respectively,

\int_{^} {v ₀} ϕ (u ₀) \cdot w < 2 and u ₀ < \infty) . (2)

Λ_{ϕ,w}

h a s w e a k l y ∥ a ∥ l s t r u c t u r e if and o n l y if

∫_0^{v₀} ϕ(u₀)· w < 2!$!.

Keywords

ENG

Lorentz-Orlicz space, normal sturcture, order continuous, Young function

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Title

Normal structure of Lorentz-Orlicz spaces

Affiliations

Abstract

Keywords

Bibliography