In this paper, we introduce the notion of sesquilinear map on Β(H) . Based on this notion, we define the quadratic map, which is the generalization of positive linear map. With the help of this concept, we prove several well-known equality and inequality...  

Let A be a Hermitian matrix, let be a normalized positive linear map and let f be a continuous real valued function. Real constants and such that (f(A)) f(((A)) (f(A)) are determined. If f is matrix convex then can be taken to be 1. A uniied approach is proposed so that the problem of determining and is reduced to solving a single variable convex minimization problem. As an illustration, the re...

let $mathcal {a} $ and $mathcal {b} $ be c$^*$-algebras. assume that $mathcal {a}$ is of real rank zero and unital with unit $i$ and $k>0$ is a real number. it is shown that if $phi:mathcal{a} tomathcal{b}$ is an additive map preserving $|cdot|^k$ for all normal elements; that is, $phi(|a|^k)=|phi(a)|^k $ for all normal elements $ainmathcal a$, $phi(i)$ is a projection, and there exists a posit...

We introduce non{autonomous well{posed and (absolutely) regular linear systems as quadrupels consisting of an evolution family and output, input and input{ output maps subject to natural hypotheses. In the spirit of G. Weiss' work these maps are represented in terms of admissible observation and control operators (the latter in an approximative sense) in the time domain. In this setting the clo...

Let $mathcal {A} $ and $mathcal {B} $ be C$^*$-algebras. Assume that $mathcal {A}$ is of real rank zero and unital with unit $I$ and $k>0$ is a real number. It is shown that if $Phi:mathcal{A} tomathcal{B}$ is an additive map preserving $|cdot|^k$ for all normal elements; that is, $Phi(|A|^k)=|Phi(A)|^k $ for all normal elements $Ainmathcal A$, $Phi(I)$ is a projection, and there exists a posit...

The order relation on the set of completely n-positive linear maps from a pro-C-algebra A to L(H), the C-algebra of bounded linear operators on a Hilbert space H, is characterized in terms of the representation associated with each completely n-positive linear map. Also, the pure elements in the set of all completely n-positive linear maps from A to L(H) and the extreme points in the set of uni...