Characterizing centralizer maps and Jordan centralizer maps through zero productsCharacterizing centralizer maps and Jordan...

Let A be an algebra and M be an A-bimodule. The main results show, under some conditions, that centralizer maps or Jordan centralizer maps ϕ:A⟶M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi :A\longrightarrow M$$\end{document} through the action on zero products are centralizer maps. These results are applied to some algebras such as 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 and the algebras generated by idempotents.