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Extreme n-positive linear maps

Published online by Cambridge University Press:  20 January 2009

Sze-Kai Tsui
Sze-Kai Tsui
Affiliation:
Department of Mathematical SciencesOakland UniversityRochesterMichigan 48309-4401, U.S.A.
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Abstract

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In this article we prove that if a completely positive linear map Φ of a unital C*-algebra A into another B with only finite dimensional irreducible representations is pure, then we have NΦ = Φker + kerΦ, where NΦ={x∈A|Φ(x) = 0}, Φker = {x∈A|Φ(x*x) = 0}, and kerΦ={x∈A|Φ(xx*) = 0}. We also prove that for every unital strongly positive and n-positive linear map Φ of a C*-algebra A onto another B with n≧2, if NΦ = Φker + kerΦ, then Φ is extreme in Pn(A, B, IB). By this null-kernel condition, many new extreme n-positive linear maps are identified. A general procedure for constructing extreme n-positive linear maps is suggested and discussed.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 36 , Issue 1 , February 1993 , pp. 123 - 131
Copyright
Copyright © Edinburgh Mathematical Society 1993

References

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