Fréchet 代数中 Michael 问题的一个解

中文摘要 AI 辅助

我们证明了交换复完备 Hausdorff 局部乘凸代数（不必含单位元）上的每个特征在有界集上有界。因此，交换复 Fréchet–Arens–Michael 代数上的每个特征连续，从而对 Michael 问题给出肯定回答。在 Fréchet 情形，每个特征被任意递增的次乘半范数定义序列中的某个半范数所控制。

英文摘要

We prove that every character on a commutative complex complete Hausdorff locally multiplicatively convex algebra, not necessarily unital, is bounded on bounded sets. Consequently, every character on a commutative complex Fréchet--Arens--Michael algebra is continuous, giving an affirmative answer to Michael's problem. In the Fréchet case, each character is bounded by one seminorm from any increasing defining sequence of submultiplicative seminorms.

发表机构

• Lancaster University（兰卡斯特大学）

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