On the geometry of positive maps in matrix algebras

DOI10.1007/BF01162009zbMath0511.46050MaRDI QIDQ1838684

Jun Tomiyama, Toshiyuki Takasaki

Publication date: 1983

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/173348

zbMATH Keywords

minimal completely positive decompositionspositive maps in matrix algebras

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) General theory of (C^*)-algebras (46L05) Linear operators in (C^*)- or von Neumann algebras (47C15)

Related Items

Quantum dynamical semigroups, symmetry groups, and locality, On the geometry of positive maps in matrix algebras. II, Positive maps and entanglement in real Hilbert spaces, A class of optimal positive maps in \(M_n\), On characteristic forms of positive vector bundles, mixed discriminants, and pushforward identities, Characterization of equivariant maps and application to entanglement detection, Completely positive module maps and completely positive extreme maps, The Unique Representation of a Selfadjoint Bounded Linear Functional, Relations Between Quantum Maps and Quantum States, On some inequalities related to positive block matrices, A Grüss inequality for \(n\)-positive linear maps, DUALITIES AND POSITIVITY IN THE STUDY OF QUANTUM ENTANGLEMENT, Cones of positive maps and their duality relations, Spectral conditions for positive maps, A family of norms with applications in quantum information theory, Recent development of the theory of completely bounded maps between \(C^*\)-algebras, Compositions and tensor products of linear maps between matrix algebras, The structural physical approximations and optimal entanglement witnesses, Positive maps from irreducibly covariant operators, \(k\) positivity and Schwarz inequality for two linear maps

Cites Work

• Recent development of the theory of completely bounded maps between \(C^*\)-algebras
• The \(W^*\)-dynamical system associated with a \(C^*\)-dynamical system, and unbounded derivations
• Ein operatorwertiger Hahn-Banach Satz
• On the Transpose Map of Matrix Algebras
• Completely Bounded Maps on C ∗ -Algebras and Invariant Operator Ranges
• Positive Linear Maps on C^*-Algebras