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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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A Class of Linear Positive Maps in Matrix Algebras II
Open Systems & Information Dynamics, 2004We provide a class of linear trace preserving positive maps on matrix algebras which is a generalization of that in [7]. A systematic construction by means of spectra of generators of SU (n) is discussed.
Gen Kimura, Andrzej Kossakowski
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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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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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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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Positive Linear Maps and the Lyapunov Equation
2002It is well-known that positivity plays an important role in the study of the discrete time and the continuous time Lyapunov equations. We show how general theorems on positive linear maps on matrices may be used in this context. Our method leads to several old, recent, and new bounds on the sensitivity of these equations.
Rajendra Bhatia, Ludwig Elsner
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On a class of linear maps and their positive invertibility
Russian Mathematical Surveys, 1996Let \(X\) and \(Y\) be separable locally convex topological spaces, \(E\) a subspace of \(X\). The author considers the class \(\Omega\) of linear maps \(T_{\alpha}: E \rightarrow Y\) (with domain of definition \(D(T_{\alpha})=E\) and taking values in \(Y\)) of the form \(T_{\alpha}=B-A_{\alpha}\) under the assumption that \(\Omega\) contains at least ...
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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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Some inequalities involving eigenvalues and positive linear maps
Advances in Operator Theory, 2023Rajesh Sharma, Ravinder Kumar
exaly
Discrete and Extremal Positive Linear Mappings
Journal of the London Mathematical Society, 1969openaire +1 more source