Let H be a complex Hilbert space. Denote by B(H)+ the set of all positive bounded linear operators on H. A bijective map φ : B(H)+ → B(H)+ is said to preserve Lebesgue decompositions in both directions if for any quadruple A,B,C,D of positive operators, B = C +D is an A-Lebesgue decomposition of B if and only if φ(B) = φ(C)+φ(D) is a φ(A)-Lebesgue decomposition of φ(B). It is proved that every ...

To assess the profitability of control schemes for Mycobacterium avium subspecies paratuberculosis (Map)-infection implemented in dairy herds, accurate estimates of its production effects are needed. This study aimed at quantifying the variation in milk yield of dairy cows according to their Map-infection status. The cow-status was determined by combining (i) its testing(s)-result(s) (serum ELI...

We provide a general and consistent formulation for linear subsystem quantum dynamical maps, developed from a minimal set of postulates, primary among which is a relaxation of the usual, restrictive assumption of uncorrelated initial system-bath states. We describe the space of possibilities admitted by this formulation, namely that, far from being limited to only completely positive (CP) maps,...

Let H be a complex Hilbert space. Denote by B(H)+ the set of all positive bounded linear operators on H. A bijective map φ : B(H)+ → B(H)+ is said to preserve Lebesgue decompositions in both directions if for any quadruple A,B,C,D of positive operators, B = C +D is an A-Lebesgue decomposition of B if and only if φ(B) = φ(C)+φ(D) is a φ(A)-Lebesgue decomposition of φ(B). It is proved that every ...

In this paper, we prove the operator inequalities as follows: Let [Formula: see text] be positive operators on a Hilbert space with [Formula: see text] and [Formula: see text]. Then for every positive unital linear map Φ, [Formula: see text] and [Formula: see text] Moreover, we prove Lin's conjecture when [Formula: see text].

We study various notions of multivariate functions which map families of positive semidefinite matrices or of conditionally positive semidefinite matrices into matrices of the same type. LINEAR ALGEBRA AND ITS APPLICATIONS 221:83-102 (1995) @ Elsevier Science Inc., 1995 0024-3795/95/$9.50 655 Avenue of the Americas, New York, NY 10010 SSDI 0024-3795(93)00232-O 84 C. H. FITZGERALD ET AL.