张婷,侯晋川.环同构及完全保持乘子不动点的映射[J].数学研究及应用,2019,39(1):89~100 |
环同构及完全保持乘子不动点的映射 |
Ring Isomorphisms and Complete Preservers of Fixed Points for Multipliers |
投稿时间:2018-02-20 修订日期:2018-11-08 |
DOI:10.3770/j.issn:2095-2651.2019.01.009 |
中文关键词: 完全保持问题 Banach代数 环同构 Banach空间算子 |
英文关键词:complete preserver problem Banach algebra ring isomorphism operator on Banach space |
基金项目:国家自然科学基金(Grant No.11671294). |
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中文摘要: |
令${\mathcal R}_1$, ${\mathcal R}_2$为两个含单位元$I$的环. 在${\mathcal R}_1$某些温和的假设条件下, 本文基于对完全保持乘子不动点映射的分类研究, 给出${\mathcal R}_1$到${\mathcal R}_2$的环同态和环同构的刻画. 然后给出在Banach代数、套代数、矩阵代数以及标准算子代数等算子代数方面的应用. |
英文摘要: |
Let ${\mathcal R}_1$ and ${\mathcal R}_2$ be two rings with unit $I$. We give some characterizations of ring homomorphisms and ring isomorphisms between ${\mathcal R}_1$ and ${\mathcal R}_2$ in term of complete preservers of fixed points of multipliers, under some mild assumption on ${\mathcal R}_1$. Applications to several kinds of operator algebras such as Banach algebras, nest algebras, matrix algebras and standard operator algebras are presented. |
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