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On certain pairs of automorphisms of C*-algebras

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  09 April 2009

C. J. K. Batty
C. J. K. Batty
Affiliation:
St. John's CollegeOxford OX1 3JP, England
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Abstract

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Let α and β be *-automorphisms of a C*-algebra A such that α + α β + β-1. There exist invariant ideals I1I2 and I3 of A, with II ∩ I2 ∩ I3 = {O}, containing, respectively, the range ofβ − α, the range of β − α-1, and the union of the ranges of β2 − α2 and β2 − α-2. The induced actions on the quotient algebras give a decomposition of the system (A, α, β) into systems where β = α, β = α-2 and α2 = α-2.

If α and β are one-parameter groups of *-automorphisms such that α + α-1 = β + β−1, then the corresponding result is valid, and may be strengthened to assert that I1 ∩ I2 = {0}.

These results are analogues and extensions of similar results of A. B. Thaheem et al. for von Neumann algebras and commuting automorphisms.

Keywords

automorphismvon Neumann algebraC*-algebracentral projectionidealderivation.

MSC classification

Secondary: 46L40: Automorphisms
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 46 , Issue 2 , April 1989 , pp. 197 - 211
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Awami, M. and Thaheem, A. B., ‘A short proof of a decomposition theorem of a von Neumann algebra’, Proc. Amer. Math. Soc. 92 (1984), 81–82.CrossRefGoogle Scholar
[2]Awami, M. and Thaheem, A. B., ‘A short proof of a decomposition theorem of a von Neumann algebra’, Boll. Un. Mat. Ital. A 2 (1983), 239–240.Google Scholar
[3]Haagerup, U. and Hanche-Olsen, F., ‘Tomita-Takesaki theory for Jordan algebras’, J. Operator Theory 11 (1984), 343–364.Google Scholar
[4]Haagerup, U. and Skau, C., ‘Geometric aspects of the Tomita-Takesaki theory II’, Math. Scand. 48 (1981), 241–252.CrossRefGoogle Scholar
[5]Thaheem, A. B., ‘Decomposition of a von Neumann algebra relative to a *-automorphism’, Proc. Edinburgh Math. Soc. 22 (1979), 9–10.CrossRefGoogle Scholar
[6]Thaheem, A. B., ‘Decomposition of a von Neumann algebra’, Rend. Sem. Mat. Univ. Padova 65 (1981), 1–7.Google Scholar
[7]Thaheem, A. B., van Daele, A. and Vanheeswijck, L., ‘A result on two one-parameter groups of automorphisms’, Math. Scand. 51 (1982), 261–274.CrossRefGoogle Scholar