Brešar, Matej; Fošner, Ajda; Fošner, Maja A Kleinecke-Shirokov type condition with Jordan automorphisms. (English) Zbl 1058.46506 Stud. Math. 147, No. 3, 237-242 (2001). Summary: Let \(\varphi\) be a Jordan automorphism of an algebra \({\mathcal A}\). The situation when an element \(a \in {\mathcal A}\) satisfies \(\frac{1}{2}(\varphi(a) + \varphi^{-1}(a)) = a\) is considered. The result which we obtain implies the Kleinecke-Shirokov theorem and Jacobson’s lemma. Cited in 5 Documents MSC: 46H05 General theory of topological algebras 47B47 Commutators, derivations, elementary operators, etc. 47B48 Linear operators on Banach algebras 16W20 Automorphisms and endomorphisms PDFBibTeX XMLCite \textit{M. Brešar} et al., Stud. Math. 147, No. 3, 237--242 (2001; Zbl 1058.46506) Full Text: DOI