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 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.