$*$-Jordan-type maps on $C^{*}$-algebras

Bruno Leonardo Macedo Ferreira; Bruno Tadeu Costa

$$-Jordan-type maps on $C^{}$-algebras

Operator Algebras 2020-05-26 v1

Authors: Bruno Leonardo Macedo Ferreira , Bruno Tadeu Costa

Abstract

Let $\mathfrak{A}$ and $\mathfrak{A}'$ be two $C^*$ -algebras with identities $I_{\mathfrak{A}}$ and $I_{\mathfrak{A}'}$ , respectively, and $P_1$ and $P_2 = I_{\mathfrak{A}} - P_1$ nontrivial projections in $\mathfrak{A}$ . In this paper we study the characterization of multiplicative $*$ -Jordan-type maps. In particular, if $\mathcal{M}$ is a factor von Neumann algebra then every bijective unital multiplicative $*$ -Jordan-type maps are $*$ -ring isomorphisms.

Keywords

jordan algebra c*-algebras hilbert modules

Cite

@article{arxiv.2005.11430,
  title  = {$*$-Jordan-type maps on $C^{*}$-algebras},
  author = {Bruno Leonardo Macedo Ferreira and Bruno Tadeu Costa},
  journal= {arXiv preprint arXiv:2005.11430},
  year   = {2020}
}

Comments

14 pages