Banach-Orlicz Algebras on a Locally Compact Group

Akbarbaglu, Ibrahim; Maghsoudi, S.

doi:10.1007/s00009-013-0267-z

Cited by 23 publications

(16 citation statements)

References 14 publications

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“…Since, for any f ∈ M Ψ (G), the map y → L y −1 f from G into M Ψ (G) is continuous [2], for every > 0 there exists…”

Section: Resultsmentioning

confidence: 99%

“…Let us remark that L Φ (G) is not, in general, closed under the convolution product; for more information see [1,2,12]. If G is locally compact abelian group, it was proved in [10] that L Φ (G) is closed under the convolution product if and only if lim x→0 Φ(x)/x > 0 or G is compact.…”

Section: Resultsmentioning

confidence: 99%

“…93470045). c 2015 Australian Mathematical Publishing Association Inc. 1446-7887/2015 $16.00 I. Akbarbaglu and S. Maghsoudi [2] Let us remark that Orlicz spaces are a genuine generalization of classical Lebesgue spaces. We would also like to mention [7,[19][20][21] in which certain linear topologies on Orlicz spaces and more general function spaces has been considered as well.…”

Section: Introductionmentioning

confidence: 99%

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A Convolution-Induced Topology on the Orlicz Space of a Locally Compact Group

Akbarbaglu

Maghsoudi

2015

J. Aust. Math. Soc.

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Let $G$ be a locally compact group with a fixed left Haar measure. In this paper, given a strictly positive Young function ${\rm\Phi}$, we consider $L^{{\rm\Phi}}(G)$ as a Banach left $L^{1}(G)$-module. Then we equip $L^{{\rm\Phi}}(G)$ with the strict topology induced by $L^{1}(G)$ in the sense of Sentilles and Taylor. Some properties of this locally convex topology and a comparison with weak$^{\ast }$, bounded weak$^{\ast }$ and norm topologies are presented.

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“…Since, for any f ∈ M Ψ (G), the map y → L y −1 f from G into M Ψ (G) is continuous [2], for every > 0 there exists…”

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Convolution-Induced Topology on the Orlicz Space of a Locally Compact Group

Akbarbaglu

Maghsoudi

2015

J. Aust. Math. Soc.

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“…To be more precise, if one consider an Orlicz space

L^{normalΦ} false(G false)

associated to the Young function Φ over a locally compact group G , then one could ask whether the convolution of compactly supported continuous functions on G can be extend to

L^{normalΦ} false(G false)

. However, in most cases, this happens if and only if

L^{normalΦ} false(G false)

is a subspace of

L^{1} false(G false)

, where the latter condition is rather restrictive; it forces either G to be compact or the Young function Φ to have a sublinear growth (see for details). For example, if G is not compact, then

L^{p} false(G false)

(

1 < p < \infty

) can never be an algebra under the convolution.…”

Section: Introductionmentioning

confidence: 99%

Twisted Orlicz algebras, II

Öztop

Samei

2018

Mathematische Nachrichten

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Let G be a locally compact group, let Ω ∶ × → ℂ * be a 2-cocycle, and let (Φ, Ψ) be a complementary pair of strictly increasing continuous Young functions. We continue our investigation in [14] of the algebraic properties of the Orlicz space Φ ( ) with respect to the twisted convolution ⊛ coming from Ω. We show that the twisted Orlicz algebra ( Φ ( ), ⊛ ) posses a bounded approximate identity if and only if it is unital if and only if is discrete. On the other hand, under suitable condition on Ω, ( Φ ( ), ⊛ )becomes an Arens regular, dual Banach algebra. We also look into certain cohomological properties of ( Φ ( ), ⊛ ), namely amenability and Connesamenability, and show that they rarely happen. We apply our methods to compactly generated group of polynomial growth and demonstrate that our results could be applied to variety of cases.

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“…Let us note that in comparison, the weighted Orlicz algebra L Φ w (G) has no bounded left approximate identity for nondiscrete G, while the Banach algebra L 1 w (G) always has a bounded left approximate identity. It should be noted that for w = 1, the existence of a bounded approximate identity and the semisimplicity of the Orlicz algebra L Φ (G) were studied independently by using different techniques in [1] for an N-function Φ. Note also that every N-function is a Young function.…”

Section: Introductionmentioning

confidence: 99%

Weighted Orlicz Algebras on Locally Compact Groups

Osançlıol¹,

Öztop²

2015

J. Aust. Math. Soc.

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For a locally compact group $G$ with left Haar measure and a Young function ${\rm\Phi}$, we define and study the weighted Orlicz algebra $L_{w}^{{\rm\Phi}}(G)$ with respect to convolution. We show that $L_{w}^{{\rm\Phi}}(G)$ admits no bounded approximate identity under certain conditions. We prove that a closed linear subspace $I$ of the algebra $L_{w}^{{\rm\Phi}}(G)$ is an ideal in $L_{w}^{{\rm\Phi}}(G)$ if and only if $I$ is left translation invariant. For an abelian $G$, we describe the spectrum (maximal ideal space) of the weighted Orlicz algebra and show that weighted Orlicz algebras are semisimple.

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Banach-Orlicz Algebras on a Locally Compact Group

Cited by 23 publications

References 14 publications

A Convolution-Induced Topology on the Orlicz Space of a Locally Compact Group

A Convolution-Induced Topology on the Orlicz Space of a Locally Compact Group

Twisted Orlicz algebras, II

Weighted Orlicz Algebras on Locally Compact Groups

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