关于乘法小扰动下Arens积稳定性的注记
A note on the stability of Arens products under small perturbations of multiplication
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中文总结 AI 辅助
本文研究Banach代数乘法小扰动对双对偶上Arens积的影响，证明Arens不规则性在足够小扰动下稳定，且等价于一致代数的Banach函数代数的Arens正则性在小扰动下保持稳定。
中文摘要 AI 辅助
在这篇短注记中，我们研究Banach代数$\mathcal A$乘法结构的小扰动及其对双对偶$\mathcal A^{**}$上两个Arens积的影响。我们证明，在Banach代数乘法结构的足够小扰动下，“Arens不规则”这一性质是稳定的。进一步，我们证明，对于任何等价于一致代数的Banach函数代数，在原始Banach函数代数乘法结构的小扰动下，Arens正则性是稳定的。
英文摘要
In this short note, we study the small perturbations of multiplication structure of a Banach algebra $\mathcal A$, and its impact on the two Arens products on the bidual $\mathcal A^{**}$. We show that the property of being \say{Arens irregular} is stable under sufficiently small perturbation in the multiplication structure of a Banach algebra. Further we show that for any Banach function algebra which is equivalent to a uniform algebra, the Arens regularity is stable under small perturbation on the multiplication structure of the original Banach function algebra.
