Characterization of n-Jordan Homomorphisms and Automatic Continuity of 3-Jordan Homomorphisms on Banach Algebras

被引：0
作者：
A. Zivari-Kazempour
机构：
[1] Ayatollah Borujerdi University,Department of Mathematics
来源：
Iranian Journal of Science and Technology, Transactions A: Science | 2020年 / 44卷
关键词：
-Homomorphism; -Jordan homomorphism; Automatic continuity; -Jordan functionally continuous; Semisimple; Primary 47B48; Secondary 46L05; 46H25;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We show that every Banach algebra A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {A}}$$\end{document} is 3-Jordan functionally continuous. More especially, every 3-Jordan homomorphism from a Banach algebra A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {A}}$$\end{document} into a commutative semisimple Banach algebra B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {B}}$$\end{document} is automatically continuous. We also prove the same result for n-Jordan homomorphism (n⩾4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\geqslant 4$$\end{document}) with the additional hypothesis that the Banach algebra A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {A}}$$\end{document} is unital. A characterization of n-Jordan homomorphism for the special case n∈{2,3,4}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\in \lbrace 2,3,4\rbrace $$\end{document} is also given.
引用
收藏
页码：213 / 218
页数：5
相关论文
共 32 条
[11]  
Karapinar E(1950)On approximate Trans Am Math Soc 69 479-502
[12]  
Gselmann E(2005)-Jordan homomorphisms J. Inequal. Appl. 2005 435-441
[13]  
Hejazian S(2009)-homomorphisms Trans Am Math Soc 361 1949-1961
[14]  
Mirzavaziri M(2015)Jordan homomorphisms Bull Malays Math Sci Soc 38 985-999
[15]  
Moslehian MS(1968)Automatic continuity of Studia Math 30 83-85
[16]  
Herstein IN(2016)-homomorphisms between Banach algebras Bull Aust Math Soc 93 301-306
[17]  
Honari TG(2018)Jordan homomorphisms of rings Asian Eur J Math 11 1-10
[18]  
Shayanpour H(2018)Hyers–Ulam–Rassias stability of Jordan homomorphisms on Banach algebras Commun Korean Math Soc 33 165-170
[19]  
Jacobson N(undefined)On the nonexistence of nontrivial involutive undefined undefined undefined-undefined
[20]  
Rickart CE(undefined)-homomorphisms of undefined undefined undefined-undefined
1234