Bibliographic Details
| 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] |
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| Database: |
Engineering Source |
