We show that the approximate quasi-orthogonality of two operator algebras is equivalent to being approximately private relative their conditional expectation quantum channels. Our analysis based on a characterization measure orthogonality in terms Choi matrices and Kraus operators for completely positive maps. present examples drawn from different areas information.

let a and b be n × m matrices. the matrix b is said to be g-row majorized (respectively g-column majorized) by a, if every row (respectively column) of b, is g-majorized by the corresponding row (respectively column) of a. in this paper all kinds of g-majorization are studied on mn,m, and the possible structure of their linear preservers will be found. also all linear operators t : mn,m ---> mn...

In this paper, we will use the categorical approach to Hilbert \(C^{\ast}\)-modules over a commutative \(C^{\ast}\)-algebra investigate approximately orthogonality preserving mappings on \(C^{\ast}\)-algebra. Indeed, show that if \(\Psi:\Gamma \rightarrow \Gamma^{\prime} \) is nonzero \( C_{0}(Z) \)-linear \(( \delta , \varepsilon)\)-orthogonality mapping between continuous fields of spaces loc...