Results 271 to 280 of about 335,000 (300)

Positive Linear Maps and Spreads of Matrices

The American Mathematical Monthly, 2014
The farther a normal matrix is from being a scalar, the more dispersed its eigenvalues should be. There are several inequalities in matrix analysis that render this principle more precise.
Rajendra Bhatia, Rajesh Sharma
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Linear mappings preserving the completely positive rank

European Journal of Combinatorics, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Operator Inequalities for Positive Linear Maps

2021
The 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, Nahid Gharakhanlu, Themistocles M. Rassias, Reza Saadati   +3 more
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A Class of Linear Positive Maps in Matrix Algebras II

Open Systems & Information Dynamics, 2004
We 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, 1972
The 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

1986
Publisher 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, 1994
We 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

2002
It 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, 1996
Let \(X\) 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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Discrete and Extremal Positive Linear Mappings

Journal of the London Mathematical Society, 1969
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