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On certain porous sets in the Orlicz space of a locally compact group

100%

Akbarbaglu I., Maghsoudi S.

Colloquium Mathematicum

2012

tom 129

nr 1

99-111

Let G be a locally compact group with a fixed left Haar measure. Given Young functions φ and ψ, we consider the Orlicz spaces $L^{φ}(G)$ and $L^{ψ}(G)$ on a non-unimodular group G, and, among other things, we prove that under mild conditions on φ and ψ, the set {$(f,g) ∈ L^{φ}(G) × L^{ψ}(G): f*g$ is well defined on G} is σ-c-lower porous in $L^{φ}(G) × L^{ψ}(G)$. This answers a question raised by Głąb and Strobin in 2010 in a more general setting of Orlicz spaces. We also prove a similar result for non-compact locally compact groups.

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

81%

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 Colloquium Mathematicum

1 Studia Mathematica

2 Akbarbaglu I.

2 Maghsoudi S.

1 Aghababa H.

1 2013

1 2012

Wyniki wyszukiwania

On certain porous sets in the Orlicz space of a locally compact group

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