Sentence examples for positive map from inspiring English sources

Let a be a self-adjoint element of an exact C*-algebra A and θ: A→A a contractive completely positive map.

From the preceding discussion (above the proof of this lemma), φ uniquely extends to a positive map on (mathcal{A}+Jmathcal{A}).

We introduce a necessary condition for a state to be separable and apply this condition to the structural physical approximation of an optimal positive map and give a proof of the fact that the SPA need not be separable.

We prove that a necessary and sufficient condition for a given partially positive matrix to have a positive completion is that a certain Schur product map defined on a certain subspace of matrices is a positive map.

We put Ψ the restriction of Φ to the C ∗ -algebra C ∗ ( A, I ) generated by I and A. Then Ψ is a unital completely positive map on C ∗ ( A, I ).

These "finitely correlated states" are explicitly constructed in terms of a finite dimensional auxiliary algebra B and a completely positive map E: A⊗B → B. We show that such a state ω is pure if and only if it is extremal periodic and its entropy density vanishes.

The proof is by contradiction and uses infinite products of completely positive maps, regarded as correspondences.

In this way, we present holomorphic geometric models for the Stinespring dilations of completely positive maps.

We study some factorisation and dilation properties of completely positive maps on noncommutative Lp-spaces.

A numerical index is introduced for semigroups of completely positive maps of B(H) which generalizes the index ofE0-semigroups.

We study positive maps of B(K) into B(H) for finite-dimensional Hilbert spaces K and H.