Perron-Frobenius Theory for Positive Maps on Trace Ideals

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dc.creatorSchrader, Robert
dc.date2000-07-14
dc.date.accessioned2026-07-07T04:27:53Z
dc.date.available2026-07-07T04:27:53Z
dc.descriptionThis article provides sufficient conditions for positive maps on the Schatten classes $\mathcal J_{p}, 1\le p<\infty$ 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 $\mathcal J_{1}$, 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.
dc.description15 pages AMS-latex, submitted for Publication to the Fields Institute Communication Series in a volume dedicated to the 60th Birthday of Sergio Doplicher and John Roberts
dc.identifierhttps://arxiv.org/abs/math-ph/0007020
dc.identifierhttp://arxiv.org/abs/math-ph/0007020
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/56586
dc.subjectMathematical Physics
dc.titlePerron-Frobenius Theory for Positive Maps on Trace Ideals
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