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

• Autorzy: Hasan P. Aghababa , Ibrahim Akbarbaglu , Saeid Maghsoudi
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 43A15: L p -spaces and other function spaces on groups, semigroups, etc.
• 47L10: Algebras of operators on Banach spaces and other topological linear spaces
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 219
• Numer: 1
• Strony: 19-34

Daty

wydano

2013

Twórcy

autor

Hasan P. Aghababa

• Department of Mathematics, University of Tabriz, Tabriz, Iran

autor

Ibrahim Akbarbaglu

• Department of Mathematics, University of Zanjan, Zanjan 45195-313, Iran

autor

Saeid Maghsoudi

• Department of Mathematics, University of Zanjan, Zanjan 45195-313, Iran

Identyfikatory

DOI

10.4064/sm219-1-2