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

Hasan P. Aghababa, Ibrahim Akbarbaglu, and Saeid Maghsoudi. "The space of multipliers and convolutors of Orlicz spaces on a locally compact group." Studia Mathematica 219.1 (2013): 19-34. <http://eudml.org/doc/286224>.

@article{HasanP2013,
abstract = {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.},
author = {Hasan P. Aghababa, Ibrahim Akbarbaglu, Saeid Maghsoudi},
journal = {Studia Mathematica},
keywords = {Orlicz space; multiplier; convolutor; -function; projective tensor product; amenable group},
language = {eng},
number = {1},
pages = {19-34},
title = {The space of multipliers and convolutors of Orlicz spaces on a locally compact group},
url = {http://eudml.org/doc/286224},
volume = {219},
year = {2013},
}

TY - JOUR
AU - Hasan P. Aghababa
AU - Ibrahim Akbarbaglu
AU - Saeid Maghsoudi
TI - The space of multipliers and convolutors of Orlicz spaces on a locally compact group
JO - Studia Mathematica
PY - 2013
VL - 219
IS - 1
SP - 19
EP - 34
AB - 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.
LA - eng
KW - Orlicz space; multiplier; convolutor; -function; projective tensor product; amenable group
UR - http://eudml.org/doc/286224
ER -