A Kleinecke–Shirokov type condition with Jordan automorphisms
Volume 147 / 2001
Studia Mathematica 147 (2001), 237-242
MSC: 46H05, 47B47, 47B48, 16W20.
DOI: 10.4064/sm147-3-3
Abstract
Let $\varphi $ be a Jordan automorphism of an algebra ${\cal A}$. The situation when an element $a\in {\cal A}$ satisfies ${1\over 2}(\varphi (a) + \varphi ^{-1}(a)) = a$ is considered. The result which we obtain implies the Kleinecke–Shirokov theorem and Jacobson's lemma.
