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The Non-m-Positive Dimension of a Positive Linear Map [PDF]
Quantum, 2019 We introduce a property of a matrix-valued linear map $\Phi$ that we call its ``non-m-positive dimension'' (or ``non-mP dimension'' for short), which measures how large a subspace can be if every quantum state supported on the subspace is non-positive ...
Nathaniel Johnston +2 more
doaj +7 more sources
On the Russo-Dye Theorem for positive linear maps [PDF]
Linear Algebra and its Applications, 2019 International audienceWe revisit a classical result, the Russo-Dye Theorem, stating that every positive linear map attains its norm at the ...
Eun-Young Lee +3 more
core +7 more sources
Further generalizations of some operator inequalities involving positive linear map
Filomat, 2017 We obtain a generalized conclusion based on an ?-geometric mean inequality. The conclusion is presented as follows: If m1,M1,m2,M2 are positive real numbers, 0 < m1 ? A ? M1 and 0 < m2 ? B ? M2 for m1 < M1 and m2 < M2, then for every
Changsen Yang, Yang Changsen
exaly +3 more sources
Completely positive linear maps on complex matrices
Linear Algebra and Its Applications, 1975 A linear map Φ from Mn to Mm is completely positive iff it admits an expression Φ(A)=ΣiV∗iAVi where Vi are n×m ...
Man-Duen Choi
exaly +3 more sources
A Grüss inequality for n-positive linear maps [PDF]
Linear Algebra and its Applications, 2010 Let A be a unital C∗-algebra and let Φ:A→B(H) be a unital n-positive linear map between C∗-algebras for some n⩾3. We show that‖Φ(AB)-Φ(A)Φ(B)‖⩽Δ(A,||·||)Δ(B,||·||)for all operators A,B∈A, where Δ(C,‖·‖) denotes the operator norm distance of C from the ...
Rajna Rajić +3 more
core +6 more sources
Linear Algebra and Its Applications, 2007 In the setting of Euclidean Jordan algebras, we study the Lipschitz continuity of the solution map of linear complementarity problems. We show that if the solution map is Lipschitz continuous and if the linear transformation has the Q-property, then the ...
Balaji, R.
exaly +3 more sources
Discrete-Time k-Positive Linear Systems [PDF]
IEEE Transactions on Automatic Control, 2021 Positive systems play an important role in systems and control theory and have found applications in multiagent systems, neural networks, systems biology, and more. Positive systems map the nonnegative orthant to itself (and also the non-positive orthant
Alseidi, Rola +2 more
core +2 more sources
Tracial positive linear maps of 𝐶*-algebras [PDF]
Proceedings of the American Mathematical Society, 1983 A positive linear map Φ : A → B \Phi :\mathfrak {A} \to \mathfrak {B} between two C ∗ {C^ * } -algebras is said to ...
Man Duen Choi, Sze Kai Tsui
core +3 more sources
Inequalities for sector matrices and positive linear maps
The Electronic Journal of Linear Algebra, 2019 Ando proved that if A, B are positive definite, then for any positive linear map Φ, it holds Φ(A#λB) ≤ Φ(A)#λΦ(B), where A#λB, 0 ≤ λ ≤ 1, means the weighted geometric mean of A, B.
Che, Huimin, Tan, Fuping
core +2 more sources
Positive linear maps on normal matrices [PDF]
International Journal of Mathematics, 2018 For a positive linear map [Formula: see text] and a normal matrix [Formula: see text], we show that [Formula: see text] is bounded by some simple linear combinations in the unitary orbit of [Formula: see text]. Several elegant sharp inequalities are derived, for instance for the Schur product of two normal matrices [Formula: see text], [Formula: see ...
Jean-Christophe Bourin, Eun-Young Lee
openaire +5 more sources