| Ring Isomorphisms and Complete Preservers of Fixed Points for Multipliers |
| Received:February 20, 2018 Revised:November 08, 2018 |
| Key Words:
complete preserver problem Banach algebra ring isomorphism operator on Banach space
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11671294). |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2019.01.009 |
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