Let G be a locally compact group and let $\omega $ be a continuous weight on G. In this paper, we first characterize bicontinuous biseparating algebra isomorphisms between weighted $L^p$ -algebras. As a result, we extend previous results of Edwards, Parrott, and Strichartz on algebra isomorphisms between $L^p$ -algebras to the setting of weighted $L^p$ -algebras. We then study the automorphisms of certain weighted $L^p$ -algebras on integers, applying known results on composition operators to classical function spaces.

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关于加权-代数之间的同构

令G为局部紧群，令 $\omega $ 为G上的连续权重。在本文中，我们首先描述了加权 $L^p$ - 代数之间的双连续双分离代数同构 。因此，我们将 Edwards、Parrott 和 Strichartz 先前关于 $L^p$ -algebras之间的代数同构的结果扩展 到加权 $L^p$ -algebras 的设置。然后，我们研究了某些加权 $L^p$ - 代数在整数上的自同构 ，将组合运算符的已知结果应用于经典函数空间。