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Normal structure of Lorentz-Orlicz spaces

100%

Lin P.-K., Sun H.

Annales Polonici Mathematici

1997

tom 67

nr 2

147-168

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 $∫_0^{v₀} ϕ(u₀)· w < 2$.

Isometries of Musielak-Orlicz spaces II

81%

Jamison J. E., Kamińska A., Lin P.-K.

Studia Mathematica

1993

tom 104

nr 1

75-89

A characterization of isometries of complex Musielak-Orlicz spaces $L_Φ$ is given. If $L_Φ$ is not a Hilbert space and $U : L_Φ → L_Φ$ is a surjective isometry, then there exist a regular set isomorphism τ from (T,Σ,μ) onto itself and a measurable function w such that U(f) = w ·(f ∘ τ) for all $f ∈ L_Φ$. Isometries of real Nakano spaces, a particular case of Musielak-Orlicz spaces, are also studied.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Studia Mathematica

2 Lin P.-K.

1 Jamison J. E.

1 Kamińska A.

1 Sun H.

1 1997

1 1993

Wyniki wyszukiwania

Normal structure of Lorentz-Orlicz spaces

Isometries of Musielak-Orlicz spaces II