Maps Preserving Product A∗B+B∗A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A^*B+B^*A$$\end{document} on C∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^*$$\end{document}-Algebras

被引:0
作者
Ali Taghavi
Saeed Gholampoor
机构
[1] University of Mazandaran,Department of Mathematics, Faculty of Mathematical Sciences
关键词
Absolute value; -algebra; -linear; Conjugate ; -linear; Homomorphism; Linear preserver problem; 47B48; 46L10;
D O I
10.1007/s41980-021-00544-4
中图分类号
学科分类号
摘要
Let 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} and 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} be two unital C∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^*$$\end{document}-algebras. It is shown that if a surjective map Φ:A→B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \Phi : \mathcal {A} \rightarrow \mathcal {B}$$\end{document} satisfies: ΦA∗B+B∗A2=Φ(A)∗Φ(B)+Φ(B)∗Φ(A)2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \Phi \left( \frac{A^*B+B^*A}{2}\right) =\frac{\Phi (A)^*\Phi (B)+ \Phi (B)^*\Phi (A)}{2} \end{aligned}$$\end{document}for every A,B∈A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A,B \in \mathcal {A}$$\end{document}, and if Φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \Phi $$\end{document} is injective or Φ(-I)=-I\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \Phi (-I)=-I $$\end{document}, then Φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Phi $$\end{document} is the direct sum of two ∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$*$$\end{document}-homomorphisms, one of which is C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {C}}$$\end{document}-linear and the other is conjugate C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {C}}$$\end{document}-linear.
引用
收藏
页码:757 / 767
页数:10
相关论文
共 48 条
[1]  
Cui J(2009)Maps preserving product Linear Algebra Appl. 431 833-842
[2]  
Li CK(2014) on factor von Neumann algebras J. Math. Anal. Appl. 409 180-188
[3]  
Dai L(2018)Nonlinear maps preserving Jordan Linear Algebra Appl. 554 86-119
[4]  
Lu F(1988)-products Publ. Res. Inst. Math. Sci. 24 707-722
[5]  
Essaleh ABA(1986)Preservers of Bull. Lond. Math. Soc. 18 51-56
[6]  
Peralta AM(1986)-Aluthge transforms Proc. Amer. Math. Soc. 96 413-420
[7]  
Friedman Y(1986)Additivity of quadratic maps J. Math. Soc. Japan 38 403-408
[8]  
Hakeda J(2015)Additivity of Linear Multilinear Algebra 63 1026-1036
[9]  
Hakeda J(2013)-semigroup isomorphisms among Linear Algebra Appl. 438 2339-2345
[10]  
Hakeda J(2016)-algebras Ann. Funct. Anal. 7 496-507