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Operator Inequalities for Positive Linear Maps
2021The main purpose of this chapter is to select the main results on squaring reverse arithmetic-geometric mean operator inequality and the reverse Ando’s operator inequality. We gathered the most important topics that showed the essential techniques to squaring operator inequalities and their p-power.
Mohammad Bagher Ghaemi +3 more
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Non-Linear Completely Positive Maps
1986Publisher Summary This chapter describes a general notion of complete positivity for (nonlinear) maps between C*-algebras, which reduces to the usual complete positivity in the case of linear maps. Every completely positive map is uniquely decomposed to ones with mixed homogenuity, each of which can be represented by means of *-representations, just ...
T. Ando, M.-D. Choi
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Positive Linear Maps on C*-Algebras
Canadian Journal of Mathematics, 1972The objective of this paper is to give some concrete distinctions between positive linear maps and completely positive linear maps on C*-algebras of operators.Herein, C*-algebras possess an identity and are written in German type . Capital letters A, B, C stand for operators, script letters for vector spaces, small letters x, y, z for vectors. Capital
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Positive Linear Mappings Between C*-Algebras
Canadian Mathematical Bulletin, 1995AbstractWe prove that a positive unital linear mapping from a von Neumann algebra to a unital C*-algebra is a Jordan homomorphism if it maps invertible selfadjoint elements to invertible elements, and that for any compact Hausdorff space X, all positive unital linear mappings from C(X) into a unital C*-algebra that preserve the invertibility for self ...
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Linear mappings preserving the completely positive rank
European Journal of Combinatorics, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Indecomposable Extreme Positive Linear Maps in Matrix Algebras
Bulletin of the London Mathematical Society, 1994We consider positive linear maps in the matrix algebra \(M_ n(\mathbb{C})\) over the complex field which fix diagonals. Such a map is of the form \[ X\mapsto A\circ X+ B\circ X^{\text{tr}}+ I\circ X,\quad X\in M_ n(\mathbb{C}), \] for self-adjoint matrices \(A\) and \(B\) with zero diagonals, where \(A\circ X\) (respectively \(X^{\text{tr}}\)) denotes ...
Kim, Hong-Jong, Kye, Seung-Hyeok
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Matrix inequalities involving a positive linear map
Linear and Multilinear Algebra, 1996Let A be a Hermitian matrix, let Φ be a normalized positive linear map and let f be a continuous real valued function. Real constants α and β such that are determined. If f is matrix convex then β can be taken to be 1. A unified approach is proposed so that the problem of determining α and β is reduced to solving a single variable convex minimization ...
Chi-Kwong Li, Roy Mathias
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