The main result of this paper is the extension of the Schur-Horn Theorem to infinite sequences: For two nonincreasing nonsummable sequences ξ and η that converge to 0, there exists a positive compact operator A with eigenvalue list η and diagonal sequence ξ if and only if Pn j=1 ξj ≤ Pn j=1 ηj for every n if and only if ξ = Qη for some orthostochastic matrix Q. When ξ and η are summable, requir...

We consider optimization problems of the following type: min{tr(CX) : A(X) = B,X positive semidefinite}. Here, tr(·) denotes the trace operator, C and X are symmetric n× n matrices, B is a symmetric m ×m matrix and A(·) denotes a linear operator. Such problems are called semidefinite programs and have recently become the object of considerable interest due to important connections with max-min ...

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.

An operator—in general nonlinear—associated with a pair of nonnegative matrices, is defined and some of its spectral properties studied. If the pair of matrices are a square matrix A and the identity matrix of the same order, the operator reduces to the linear operator A. The results obtained include generalizations of one of the principal conclusions of the theorem of Perron-Frobenius.