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Asymmetric invariant sets for completely positive maps on C*-algebras

Published online by Cambridge University Press:  17 April 2009

A. Guyan Robertson
A. Guyan Robertson
Affiliation:
Department of Mathematics, Edinburgh University, Mayfield Road, Edinburgh EH9 3JZ
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Abstract

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Let A be a noncommutative C*-algebra other than M2(I). We show that there exists a completely positive map φ of norm one on A and an element a ɛ A such that φ(a) = a, φ(a*a) = a*a, but φ(aa*) ≠ aa*.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 33 , Issue 3 , June 1986 , pp. 471 - 473
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Dixmier, J., C*-algebras (North-Holland Publishing Co, 1977).Google Scholar
[2]Limaye, B. V. and Namboodiri, M. N. N., ‘A generalized noncommutative Korovkin theorem”, Illinois J. Math. 28 (1984), 267–280.CrossRefGoogle Scholar
[3]Stinespring, W., “Positive functions on C *algebras”, Proc: Amer. Math. Soc. 6 (1955), 211–216.Google Scholar