A Kleinecke–Shirokov type condition with Jordan automorphisms

Volume 147 / 2001

Matej Brešar, Ajda Fošner, Maja Fošner 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.

Authors

  • Matej BrešarDepartment of Mathematics
    University of Maribor
    PF, Koroška 160
    2000 Maribor, Slovenia
    e-mail
  • Ajda FošnerDepartment of Mathematics
    University of Maribor
    PF, Koroška 160
    2000 Maribor, Slovenia
    e-mail
  • Maja FošnerInstitute of Mathematics, Physics and Mechanics
    Jadranska 19
    1000 Ljubljana, Slovenia
    e-mail

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