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Mathematical Proceedings of the Cambridge Philosophical Society Mathematical Proceedings of the Cambridge Philosophical Society

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Erratum to “Full and reduced C*-coactions”. Math. Proc. Camb. Phil. Soc. 116 (1994), 435–450

Published online by Cambridge University Press:  12 May 2016

S. KALISZEWSKI  and
JOHN QUIGG
S. KALISZEWSKI
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287, U.S.A. e-mail: kaliszewski@asu.edu; quigg@asu.edu
JOHN QUIGG
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287, U.S.A. e-mail: kaliszewski@asu.edu; quigg@asu.edu
Corresponding
E-mail address:
kaliszewski@asu.edu
quigg@asu.edu
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Proposition 2ċ5 of [5] states that a full coaction of a locally compact group on a C*-algebra is nondegenerate if and only if its normalisation is. Unfortunately, the proof there only addresses the forward implication, and we have not been able to find a proof of the opposite implication. This issue is important because the theory of crossed-product duality for coactions requires implicitly that the coactions involved be nondegenerate. Moreover, each type of coaction — full, reduced, normal, maximal, and (most recently) exotic — has its own distinctive properties with respect to duality, making it crucial to be able to convert from one to the other without losing nondegeneracy.

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Erratum
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 161 , Issue 2 , September 2016 , pp. 379 - 380
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Copyright © Cambridge Philosophical Society 2016 

References

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[3] Kwaśniewski, B. K. and Szymański, W. Topological aperiodicity for product systems over semi- groups of Ore type. (2016) doi:10.1016/j.jfa.2016.02.014.Google Scholar
[4] Landstad, M. B. Duality theory for covariant systems. Trans. Amer. Math. Soc. 248 (1979), 223–267.CrossRefGoogle Scholar
[5] Quigg, J. C. Full and reduced C*-coactions. Math. Proc. Camb. Phil. Soc. 116 (1994), 435–450.CrossRefGoogle Scholar
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Erratum to “Full and reduced C*-coactions”. Math. Proc. Camb. Phil. Soc. 116 (1994), 435–450
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Erratum to “Full and reduced C*-coactions”. Math. Proc. Camb. Phil. Soc. 116 (1994), 435–450
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