Perron-frobenius Theory for Positive Maps on Trace Ideals
نویسنده
چکیده
This article provides sufficient conditions for positive maps on the Schatten classes Jp; 1 p < 1 of bounded operators on a separable Hilbert space such that a corresponding Perron-Frobenius theorem holds. With applications in quantum information theory in mind sufficient conditions are given for a trace preserving, positive map on J1, the space of trace class operators, to have a unique, strictly positive density matrix which is left invariant under the map. Conversely to any given strictly positive density matrix there are trace preserving, positive maps for which the density matrix is the unique Perron-Frobenius vector. Dedicated to S. Doplicher and J.E. Roberts on the occasion of their 60th birthday
منابع مشابه
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