L1-Algebras and Segal Algebras

Reiter, Hans

doi:10.1007/bfb0060759

Cited by 132 publications

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“…Reiter established classical Segal algebras in his monograph [12]. A Segal algebra S 1 (G) on a locally compact group G is a dense left ideal of L 1 (G) that satisfies the following conditions: Equipped with the norm || · || S and the convolution product, denoted by f, S 1 (G) is a Banach algebra.…”

Section: Introductionmentioning

confidence: 99%

Approximate Identities for Ideals of Segal Algebras on A Compact Group

Zhang¹

2002

Journal of Functional Analysis

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We show that every closed ideal of a Segal algebra on a compact group admits a central approximate identity which has the property, called condition (U), that the induced multiplication operators converge to the identity operator uniformly on compact sets of the ideal. This result extends a known one due to H. Reiter who has considered the problem under the condition that the Segal algebra is symmetric. We prove further that a closed right ideal of a Segal algebra on a compact group admits a left approximate identity satisfying condition (U) if and only if it is approximately complemented as a subspace of the Segal algebra; if in addition the Segal algebra is symmetric, then a closed left ideal admits a right approximate identity satisfying condition (U) if and only if it is approximately complemented. © 2002 Elsevier Science (USA)

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Section: Introductionmentioning

confidence: 99%

Approximate Identities for Ideals of Segal Algebras on A Compact Group

Zhang¹

2002

Journal of Functional Analysis

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“…In fact all of the obtained results about L 1,p ω (G), can be considered as the consequences for Segal algebra [20] for basic definitions and information concerning Segal algebras.…”

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confidence: 87%

Pseudo-contractibility Of Weighted Lp -Algebras

Abtahi

2013

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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“…This condition was introduced by Reiter [21], [22] in the group case and later studied by Skantharajah [23] in the context of hypergroups.…”

Section: Existence Of Bounded Approximate Identitiesmentioning

confidence: 99%

Reiter?s Condition P1 and Approximate Identities for Polynomial Hypergroups

Filbir

Lasser

Szwarc³

2004

Monatsh. Math.

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Abstract. Let K be a commutative hypergroup with the Haar measure . In the present paper we investigate whether the maximal ideals in L 1 ðK; Þ have bounded approximate identities. We will show that the existence of a bounded approximate identity is equivalent to the existence of certain functionals on the space L 1 ðK; Þ. Finally we apply the results to polynomial hypergroups and obtain a rather complete solution for this class.

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L1-Algebras and Segal Algebras

Cited by 132 publications

References 0 publications

Approximate Identities for Ideals of Segal Algebras on A Compact Group

Approximate Identities for Ideals of Segal Algebras on A Compact Group

Pseudo-contractibility Of Weighted Lp -Algebras

Reiter?s Condition P1 and Approximate Identities for Polynomial Hypergroups

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