Ring Isomorphisms and Complete Preservers of Fixed Points for Multipliers
Received:February 20, 2018  Revised:November 08, 2018
Key Word: complete preserver problem   Banach algebra   ring isomorphism   operator on Banach space
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11671294).
 Author Name Affiliation Ting ZHANG School of Mathematics, Taiyuan University of Technology, Shanxi 030024, P. R. China Department of Mathematics, Shanxi University, Shanxi 030006, P. R. China Jinchuan HOU School of Mathematics, Taiyuan University of Technology, Shanxi 030024, P. R. China
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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.