Let $${\mathcal {S}}$$ S be a compactly cancellative foundation semigroup with identity and $$M_a({\mathcal {S}})$$ M a ( S ) be its semigroup algebra. In this paper, we give some characterizations for $$ {{\mathfrak {Q}}}{{\mathfrak {M}}}(M_a({\mathcal {S}}))$$ Q M ( M a ( S ) ) , the quasi-multipliers of $$M_a({\mathcal {S}})$$ M a ( S ) . It is shown that $$ {{\mathfrak {Q}}}{{\mathfrak {M}}}(M_a({\mathcal {S}}))$$ Q M ( M a ( S ) ) may be identified by $$M({\mathcal {S}})$$ M ( S ) . We deal with the quasi-multipliers on the dual Banach algebra $$L_{0}^{\infty }({\mathcal {S}};M_a({\mathcal {S}}))$$ L 0 ∞ ( S ; M a ( S ) ) and prove that its quasi-multipliers is again $$M({\mathcal {S}})$$ M ( S ) . We also discuss the bilinear mappings $${\mathfrak {m}} :M_a({\mathcal {S}})^{*} \times M_a({\mathcal {S}})^{*} \longrightarrow M_a({\mathcal {S}})^{*}$$ m : M a ( S ) ∗ × M a ( S ) ∗ ⟶ M a ( S ) ∗ which commutes with translations and convolutions.

中文翻译：

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Banach 代数上与局部紧半群相关的拟乘子

令 $${\mathcal {S}}$$ S 是一个具有恒等式的紧抵消基础半群，$$M_a({\mathcal {S}})$$ M a ( S ) 是它的半群代数。在本文中，我们给出了 $$ {{\mathfrak {Q}}}{{\mathfrak {M}}}(M_a({\mathcal {S}}))$$ QM ( M a ( S ) ) ，$$M_a({\mathcal {S}})$$ M a ( S ) 的准乘数。表明 $$ {{\mathfrak {Q}}}{{\mathfrak {M}}}(M_a({\mathcal {S}}))$$ QM ( M a ( S ) ) 可以由下式标识$$M({\mathcal {S}})$$ M ( S ) 。我们处理对偶 Banach 代数 $$L_{0}^{\infty }({\mathcal {S}};M_a({\mathcal {S}}))$$ L 0 ∞ ( S ; M a ( S ) ) 并证明它的准乘数又是 $$M({\mathcal {S}})$$ M ( S ) 。我们还讨论了双线性映射 $${\mathfrak {m}} ：