# Conditions of fixed sign for $n\times n$ operator matrices

@article{Orlov2010ConditionsOF, title={Conditions of fixed sign for \$n\times n\$ operator matrices}, author={I. Orlov and E. V. Bozhonok}, journal={arXiv: Functional Analysis}, year={2010} }

A positive definiteness criterion and, under the additional conditions, a nonnegativity criterion for a self-adjoint continuous operator matrix, acting in product of an arbitrary number of real separable Hilbert spaces, are obtained. As application, both sufficient and necessary analytical conditions of functional extremum of several Hilbert variables are considered.

## 3 Citations

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Let HA⊗HB be a bipartite system and ρAB a quantum state on HA⊗HB, ρA=TrB(ρAB), ρB=TrA(ρAB). Then each quantum operation ΦB on the quantum system HB can induce a quantum ensemble {(pμ,ρA,μ)} on…

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For a quantum ensemble $\cE_3 =\set{\Pa{p_i,\rho_i}}_{i=1}^3$, M. Fannes \emph{et al.} conjectured that the entropy of the correlation matrix of $\cE_3 =\set{\Pa{p_i,\rho_i})}_{i=1}^3$ is upper bound…

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