7 research outputs found
Rank properties of exposed positive maps
Let \cK and \cH be finite dimensional Hilbert spaces and let \fP denote
the cone of all positive linear maps acting from \fB(\cK) into \fB(\cH). We
show that each map of the form or is an
exposed point of \fP. We also show that if a map is an exposed point
of \fP then either is rank 1 non-increasing or \rank\phi(P)>1 for
any one-dimensional projection P\in\fB(\cK).Comment: 6 pages, last section removed - it will be a part of another pape