• Corpus ID: 119563946

# 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}
}
• Published 1 September 2010
• Mathematics
• arXiv: Functional Analysis
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
Universal upper bound for the Holevo information induced by a quantum operation
• Physics, Mathematics
• 2011
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
Sharply Bounding the Holevo Quantity
• Mathematics
• 2011
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

## References

SHOWING 1-10 OF 14 REFERENCES
On block diagonal and Schur complement preconditioning
SummaryWe study symmetric positive definite linear systems, with a 2-by-2 block matrix preconditioned by inverting directly one of the diagonal blocks and suitably preconditioning the other. Using an
On Krein's extension theory of nonnegative operators
• Mathematics
• 2004
In M. G. Krein's extension theory of nonnegative operators a complete description is given of all nonnegative selfadjoint extensions of a densely defined nonnegative operator. This theory, the
Compact Extrema: A General Theory and Its Applications to Variational Functionals
The general properties of compact extrema and the conditions for compact extrema in terms of the compact derivatives in Hilbert space are considered. The compact-analytical properties of and
Conservative realizations of the functions associated with Schur's algorithm for the Schur class operator-valued function
Let M and N be separable Hilbert spaces and let Θ(λ) be a function from the Schur class S(M,N) of contractive functions holomorphic on the unit disk. The operator generalization of the classical
The differential ? -calculus
We define a differential λμ-calculus which is an extension of both Parigot’s λμ-calculus and EhrhardRégnier’s differential λ-calculus. We prove some basic properties of the system: reduction enjoys
Operator Approach to Linear Problems of Hydrodynamics
• Engineering
• 2012
This book presents some of the papers presented at the XIXth Conference of the Technical Committee 7 of the International Federation of Information Processing (IFIP). It was held in Cambridge,
Compact extremum and compact analytical properties of basic variational functional in Sobolev space W 1 2
• Manuscript: The dissertations for obtaining scientific degree of candidate of physical and mathematical sciences by speciality 01.01.02. Simferopol
• 2008
Khatskevich, Bistrict plus-operators and frac- tional linear operator mappings, Ukrainian
• Mathematical Bulletin,
• 2007
Operator methods in linear hydrodynamics
• Nauka, Moscow,
• 1989