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The space of multipliers and convolutors of Orlicz spaces on a locally compact group

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Aghababa H., Akbarbaglu I., Maghsoudi S.

Studia Mathematica

2013

tom 219

nr 1

19-34

Let G be a locally compact group, let (φ,ψ) be a complementary pair of Young functions, and let $L^{φ}(G)$ and $L^{ψ}(G)$ be the corresponding Orlicz spaces. Under some conditions on φ, we will show that for a Banach $L^{φ}(G)$-submodule X of $L^{ψ}(G)$, the multiplier space $Hom_{L^{φ}(G)}(L^{φ}(G),X*)$ is a dual Banach space with predual $L^{φ}(G)∙X := \overline{span} {ux: u ∈ L^{φ}(G), x ∈ X}$, where the closure is taken in the dual space of $Hom_{L^{φ}(G)}(L^{φ}(G),X*)$. We also prove that if $φ $ is a Δ₂-regular N-function, then $Cv_{φ}(G)$, the space of convolutors of $M^{φ}(G)$, is identified with the dual of a Banach algebra of functions on G under pointwise multiplication.

Ograniczanie wyników

1 Studia Mathematica

1 Aghababa H.

1 Akbarbaglu I.

1 Maghsoudi S.

1 2013

Wyniki wyszukiwania

The space of multipliers and convolutors of Orlicz spaces on a locally compact group