Geodesic
Normal structure of Lorentz-Orlicz spaces
Annales Polonici Mathematici, Tome 67 (1997) no. 2, pp. 147-168

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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 $Λ_{ϕ,w}(0,∞)$ (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, $∫_^{v₀} ϕ(u₀) · w 2 and u₀ ∞). (2) $Λ_{ϕ,w}$ has weakly normal structure if and only if $∫_0^{v₀} ϕ(u₀)· w 2$.
DOI : 10.4064/ap-67-2-147-168
Keywords: Lorentz-Orlicz space, normal sturcture, order continuous, Young function

Pei-Kee Lin 1 ; Huiying Sun 1

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Pei-Kee Lin; Huiying Sun. Normal structure of Lorentz-Orlicz spaces. Annales Polonici Mathematici, Tome 67 (1997) no. 2, pp. 147-168. doi: 10.4064/ap-67-2-147-168

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