Thaheem, A. B. On pairs of automorphisms of von Neumann algebras. (English) Zbl 0685.46037 Int. J. Math. Math. Sci. 12, No. 2, 285-290 (1989). Let a and b be *-automorphisms of a von Neumann algebra M satisfying the operator equation \(a+a^{-1}=b+b^{-1}.\) It was known that if a and b commute then there exists a central projection p in M such that \(a=b\) on Mp and \(a=b^{-1}\) on M(I-p). In this paper, an example is given to show that the above statement may not be true when a and b do not commute. However, it is proved that if a and b satisfy the equation, then there exists a central projection p in M such that \(a^ 2=b^ 2\) on Mp and \(a^ 2=b^{-2}\) on M(I-p). This provides a general solution of the equation for von Neumann algebras. Reviewer: Hou Jinchuan MSC: 46L40 Automorphisms of selfadjoint operator algebras 47C15 Linear operators in \(C^*\)- or von Neumann algebras 46L10 General theory of von Neumann algebras Keywords:*-automorphisms; central projection PDFBibTeX XMLCite \textit{A. B. Thaheem}, Int. J. Math. Math. Sci. 12, No. 2, 285--290 (1989; Zbl 0685.46037) Full Text: DOI EuDML