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1

Normal structure of Lorentz-Orlicz spaces

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Lin P.-K., Sun H.

Annales Polonici Mathematici

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1997

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tom 67

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nr 2

147-168

EN

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 $∫_0^{v₀} ϕ(u₀)· w < 2$.

2

Reflexive Orlicz spaces have uniformly normal structure

100%

Chen S., Sun H.

Studia Mathematica

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1994

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tom 109

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nr 2

197-208

EN

We prove that an Orlicz space equipped with the Luxemburg norm has uniformly normal structure if and only if it is reflexive.

3

λ-Properties of Orlicz sequence spaces

100%

Chen S., Sun H.

Annales Polonici Mathematici

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1994

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tom 59

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nr 3

239-249

EN

It is proved that every Orlicz sequence space has the λ-property. Criteria for the uniform λ-property in Orlicz sequence spaces, with Luxemburg norm and Orlicz norm, are given.

Ograniczanie wyników

2 Annales Polonici Mathematici

1 Studia Mathematica

3 Sun H.

2 Chen S.

1 Lin P.-K.

1 1997

2 1994

Normal structure of Lorentz-Orlicz spaces

Reflexive Orlicz spaces have uniformly normal structure

λ-Properties of Orlicz sequence spaces