J Austral Math Soc Ser A 54 pp29--38, 1993.

On Certain Pairs of Automorphisms of Rings

Matej Bresar

Abstract

In this paper we prove algebraic generalizations of some results of C. J. K. Batty and A. B. Thaheem, concerning with the identity a+ a^-1 = b+ b^-1 where a and b are automorphisms of a C*-algebra. The main result asserts that if automorphisms a, b of a semiprime ring R satisfy a+ a^-1 = b+ b^-1 then there exist invariant ideals U₁, U₂ and U₃ of R such that U_i ÇU_j = 0, i ¹ j, U₁ ÅU₂ ÅU₃ is an essential ideal, a = b on U₁, a = b^-1 on U₂, and a² = b² = a^-2 on U₃. Furthermore, if the annihilator of any ideal in R is a direct summand (in particular, if R is a von Neumann algebra), then U₁ ÅU₂ ÅU₃ = R.

1991 AMS Subject Classification: primary 16W20; secondary 46L40

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Authors

Matej Bresar

University of Maribor, PF, Koroska 160, 62000 Maribor, Slovenia.