Topological centres of weighted convolution algebras.
Saved in:
| Title: | Topological centres of weighted convolution algebras. |
|---|---|
| Authors: | Filali, Mahmoud1 (AUTHOR) mahmoud.filali@oulu.fi, Salmi, Pekka1 (AUTHOR) pekka.salmi@iki.fi |
| Source: | Journal of Functional Analysis. Jun2020, Vol. 278 Issue 11, pN.PAG-N.PAG. 1p. |
| Subjects: | Algebra, Compact groups, Mathematical convolutions, Continuous groups, Topological algebras |
| Abstract: | Let G be a non-compact locally compact group with a continuous submultiplicative weight function ω such that ω (e) = 1 and ω is diagonally bounded with bound K ≥ 1. When G is σ -compact, we show that ⌊ K ⌋ + 1 many points in the spectrum of LUC (ω − 1) are enough to determine the topological centre of LUC (ω − 1) ⁎ and that ⌊ K ⌋ + 2 many points in the spectrum of L ∞ (ω − 1) are enough to determine the topological centre of L 1 (ω) ⁎ ⁎ when G is in addition a SIN-group. We deduce that the topological centre of LUC (ω − 1) ⁎ is the weighted measure algebra M (ω) and that of C 0 (ω − 1) ⊥ is trivial for any locally compact group. The topological centre of L 1 (ω) ⁎ ⁎ is L 1 (ω) and that of L 0 ∞ (ω) ⊥ is trivial for any non-compact locally compact SIN-group. The same techniques apply and lead to similar results when G is a weakly cancellative right cancellative discrete semigroup. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Functional Analysis is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 142165376 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Topological centres of weighted convolution algebras. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Filali%2C+Mahmoud%22">Filali, Mahmoud</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> mahmoud.filali@oulu.fi</i><br /><searchLink fieldCode="AR" term="%22Salmi%2C+Pekka%22">Salmi, Pekka</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> pekka.salmi@iki.fi</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Functional+Analysis%22">Journal of Functional Analysis</searchLink>. Jun2020, Vol. 278 Issue 11, pN.PAG-N.PAG. 1p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Algebra%22">Algebra</searchLink><br /><searchLink fieldCode="DE" term="%22Compact+groups%22">Compact groups</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+convolutions%22">Mathematical convolutions</searchLink><br /><searchLink fieldCode="DE" term="%22Continuous+groups%22">Continuous groups</searchLink><br /><searchLink fieldCode="DE" term="%22Topological+algebras%22">Topological algebras</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Let G be a non-compact locally compact group with a continuous submultiplicative weight function ω such that ω (e) = 1 and ω is diagonally bounded with bound K ≥ 1. When G is σ -compact, we show that ⌊ K ⌋ + 1 many points in the spectrum of LUC (ω − 1) are enough to determine the topological centre of LUC (ω − 1) ⁎ and that ⌊ K ⌋ + 2 many points in the spectrum of L ∞ (ω − 1) are enough to determine the topological centre of L 1 (ω) ⁎ ⁎ when G is in addition a SIN-group. We deduce that the topological centre of LUC (ω − 1) ⁎ is the weighted measure algebra M (ω) and that of C 0 (ω − 1) ⊥ is trivial for any locally compact group. The topological centre of L 1 (ω) ⁎ ⁎ is L 1 (ω) and that of L 0 ∞ (ω) ⊥ is trivial for any non-compact locally compact SIN-group. The same techniques apply and lead to similar results when G is a weakly cancellative right cancellative discrete semigroup. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Functional Analysis is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=142165376 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.jfa.2020.108468 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 1 StartPage: N.PAG Subjects: – SubjectFull: Algebra Type: general – SubjectFull: Compact groups Type: general – SubjectFull: Mathematical convolutions Type: general – SubjectFull: Continuous groups Type: general – SubjectFull: Topological algebras Type: general Titles: – TitleFull: Topological centres of weighted convolution algebras. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Filali, Mahmoud – PersonEntity: Name: NameFull: Salmi, Pekka IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 06 Text: Jun2020 Type: published Y: 2020 Identifiers: – Type: issn-print Value: 00221236 Numbering: – Type: volume Value: 278 – Type: issue Value: 11 Titles: – TitleFull: Journal of Functional Analysis Type: main |
| ResultId | 1 |
