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
|Author:||Filali, Mahmoud1; Salmi, Pekka1|
1University of Oulu, Research Unit of Mathematical Sciences, PL 3000, FI-90014 Oulun yliopisto, Finland
|Persistent link:|| http://urn.fi/urn:nbn:fi-fe2020051335418
|Publish Date:|| 2022-01-14
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 L1(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 C0(ω-1)┴ is trivial for any locally compact group. The topological centre of L1(ω)⁎⁎ is L1(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.
Journal of functional analysis
|Type of Publication:||
A1 Journal article – refereed
|Field of Science:||
© 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/.