$*$-Lie-type maps on $C^*$-algebras

Ruth Nascimento Ferreira; Bruno Leonardo Macedo Ferreira; Henrique Guzzo Junior; Bruno Tadeu Costa

$$-Lie-type maps on $C^$-algebras

Operator Algebras 2021-08-21 v1 Rings and Algebras

Authors: Ruth Nascimento Ferreira , Bruno Leonardo Macedo Ferreira , Henrique Guzzo Junior , 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 symmetric projections in $\mathfrak{A}$ . In this paper we study the characterization of multiplicative $*$ -Lie-type maps. In particular, if $\mathcal{M}$ is a factor von Neumann algebra then every complex scalar multiplication bijective unital multiplicative $*$ -Lie-type map is $*$ -isomorphism.

Keywords

c*-algebras hilbert modules lie algebra

Cite

@article{arxiv.2108.00025,
  title  = {$*$-Lie-type maps on $C^*$-algebras},
  author = {Ruth Nascimento Ferreira and Bruno Leonardo Macedo Ferreira and Henrique Guzzo Junior and Bruno Tadeu Costa},
  journal= {arXiv preprint arXiv:2108.00025},
  year   = {2021}
}

Comments

15. arXiv admin note: text overlap with arXiv:2005.11430