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Original Articles

Rank properties of exposed positive maps

Pages 970-975 | Received 21 May 2012, Accepted 09 Aug 2012, Published online: 28 Sep 2012
 

Abstract

Let 𝒦 and ℋ be finite dimensional Hilbert spaces and let denote the cone of all positive linear maps acting from into . We show that each map of the form φ(X) = AXA* or φ(X) = AX T A* is an exposed point of . It is done by careful analysis of rank properties of these maps.

AMS Subject Classifications::

Acknowledgements

The research is supported partially by the research grant of MNiSW N N202 208238 and South Africa – Poland scientific cooperation project UID 72336.

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