关于导子的不连续性及其诱导的非唯一完备度量拓扑
泛函分析
2020-02-18 v1
摘要
我们给出一种简单方法，用于构造具有两种不等价 Fréchet 代数拓扑的交换 Fréchet 代数。该结果被用于表明任意非代数解析函数的行动可能未被唯一定义，以及其他有用应用。我们对 Loy 1974 年的一个问题给出肯定回答。我们还获得了具有有限维根的理想 Fréchet 代数的 Fréchet 代数拓扑的唯一性。
关键词
引用
@article{arxiv.2002.06365,
title = {On discontinuity of derivations, inducing non-unique complete metric topologies},
author = {S. R. Patel},
journal= {arXiv preprint arXiv:2002.06365},
year = {2020}
}
备注
Read used "tensor product by rows" method to show that a certain algebra admits two inequivalent topology and showed that Singer-Wermer conjecture fails in the Frechet case. We study discontinuity of derivation/functional in detail. The 2nd paper gives examples with countably many inequivalent topologies; the 2nd example satisfies this conjecture, and admits countably many equivalent topologies