Completely positive linear maps on complex matrices

Linear maps preserving or strongly preserving majorization on matrices

For $A,Bin M_{nm},$ we say that $A$ is left matrix majorized (resp. left matrix submajorized) by $B$ and write $Aprec_{ell}B$ (resp. $Aprec_{ell s}B$), if $A=RB$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $R.$ Moreover, we define the relation $sim_{ell s} $ on $M_{nm}$ as follows: $Asim_{ell s} B$ if $Aprec_{ell s} Bprec_{ell s} A.$ This paper characterizes all linear p...

Positive Linear Maps and Spreads of Matrices

Covariant Completely Positive Linear Maps between Locally C-algebras

We prove a covariant version of the KSGNS (Kasparov, Stinespring, Gel’fand,Naimark,Segal) construction for completely positive linear maps between locally C-algebras. As an application of this construction, we show that a covariant completely positive linear map ρ from a locally C-algebra A to another locally C -algebra B with respect to a locally C-dynamical system (G,A,α) extends to a complet...

Gluing of completely positive maps

Gluings of completely positive maps (CPMs) are defined and investigated. As a brief description of this concept consider a pair of ‘evolution machines’, each with the ability to evolve the internal state of a ‘particle’ inserted into its input. Each of these machines is characterized by a channel describing the operation the internal state has experienced when the particle is returned at the ou...

Interpolation by Completely Positive Maps

Given commuting families of Hermitian matrices {A1, . . . , Ak} and {B1, . . . , Bk}, conditions for the existence of a completely positive map Φ, such that Φ(Aj) = Bj for j = 1, . . . , k, are studied. Additional properties such as unital or / and trace preserving on the map Φ are also considered. Connections of the study to dilation theory, matrix inequalities, unitary orbits, and quantum inf...