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.

中文翻译：

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加权卷积代数的拓扑中心

摘要 令 G 是一个非紧局部紧群，具有连续的乘法权重函数 ω，使得 ω ( e ) = 1 且 ω 对角有界，边界 K ≥ 1。当 G 是 σ-compact 时，我们证明 ⌊ K ⌋ + 1 个 LUC ( ω − 1 ) 谱中的多个点足以确定 LUC ( ω − 1 ) ⁎ 的拓扑中心，并且 ⌊ K ⌋ + 2 个多个点L ∞ ( ω − 1 ) 谱中的点足以确定 L 1 ( ω ) ⁎ ⁎ 的拓扑中心，当 G 是另外一个 SIN 群时。我们推导出 LUC ( ω − 1 ) ⁎ 的拓扑中心是加权测度代数 M ( ω ) 并且 C 0 ( ω − 1 ) ⊥ 的拓扑中心对于任何局部紧群都是微不足道的。L 1 ( ω ) ⁎ ⁎ 的拓扑中心是 L 1 ( ω ) 而 L 0 ∞ ( ω ) ⊥ 的拓扑中心对于任何非紧局部紧正弦群是微不足道的。