University of Oulu

Mahmoud Filali, Pekka Salmi, Topological centres of weighted convolution algebras, Journal of Functional Analysis, Volume 278, Issue 11, 2020, 108468, ISSN 0022-1236, https://doi.org/10.1016/j.jfa.2020.108468

Topological centres of weighted convolution algebras

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Author: Filali, Mahmoud1; Salmi, Pekka1
Organizations: 1University of Oulu, Research Unit of Mathematical Sciences, PL 3000, FI-90014 Oulun yliopisto, Finland
Format: article
Version: accepted version
Access: embargoed
Persistent link: http://urn.fi/urn:nbn:fi-fe2020051335418
Language: English
Published: Elsevier, 2020
Publish Date: 2022-01-14
Description:

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-1) are enough to determine the topological centre of LUC-1) and that [K] + 2 many points in the spectrum of L-1) are enough to determine the topological centre of L1(ω)⁎⁎ when G is in addition a SIN-group. We deduce that the topological centre of LUC-1) is the weighted measure algebra M(ω) and that of C0-1) is trivial for any locally compact group. The topological centre of L1(ω)⁎⁎ is L1(ω) and that of L0(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.

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Series: Journal of functional analysis
ISSN: 0022-1236
ISSN-E: 1096-0783
ISSN-L: 0022-1236
Volume: 278
Issue: 11
Article number: 108468
DOI: 10.1016/j.jfa.2020.108468
OADOI: https://oadoi.org/10.1016/j.jfa.2020.108468
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Subjects:
Copyright information: © 2020 Elsevier B.V. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/.
  https://creativecommons.org/licenses/by-nc-nd/4.0/