J Austral Math Soc Ser A 46 pp197--211, 1989.

On Certain Pairs of Automorphisms of C*-Algebras

C. J. K. Batty

Abstract

Let a and b be *-automorphisms of a C*-algebra A such that a+ a^-1 = b+ b^-1. There exist invariant ideals I₁, I₂ and I₃ of A, with I₁ ÇI₂ ÇI₃ = {0}, containing, respectively, the range of b- a, the range of b- a^-1, and the union of the ranges b² - a² and b² - a^-2. The induced actions on the quotient algebras give a decomposition of the system (A, a, b) into systems where b = a, b = a^-1 and b² = a² = a^-2. If a and b are one-parameter groups of *-automorphisms such that a+ a^-1 = b+ b^-1, then the corresponding result is valid, and may br strengthened to assert that I₁ ÇI₂ = {0}. These results are analogues and extensions of similar results of A. B. Thaheem et al. for von Neumann algebras and commuting automorphisms.

1980 AMS Subject Classification (1985 Revision): 46L40

Browse the article

Authors

C. J. K. Batty

St. John's College, Oxford OX1 3JP, England.