Characterizations of tracial property via inequalities.
Computing the determinantal representations of hyperbolic forms
The numerical range of an matrix is determined by an degree hyperbolic ternary form. Helton-Vinnikov confirmed conversely that an degree hyperbolic ternary form admits a symmetric determinantal representation. We determine the types of Riemann theta functions appearing in the Helton-Vinnikov formula for the real symmetric determinantal representation of hyperbolic forms for the genus . We reformulate the Fiedler-Helton-Vinnikov formulae for the genus , and present an elementary computation...
Computing the numerical range of Krein space operators
Consider the Hilbert space (H,〈• , •〉) equipped with the indefinite inner product[u,v]=v*J u,u,v∈ H, where J is an indefinite self-adjoint involution acting on H. The Krein space numerical range WJ(T) of an operator T acting on H is the set of all the values attained by the quadratic form [Tu,u], with u ∈H satisfying [u,u]=± 1. We develop, implement and test an alternative algorithm to compute WJ(T) in the finite dimensional case, constructing 2 by 2 matrix compressions of T and their easily determined...
Continuite lipschitzienne du spectre comme fonction d'un opérateur normal
Convergence of -norms of a matrix
a recurrence relation for computing the -norms of an Hermitian matrix is derived and an expression giving approximately the number of eigenvalues which in absolute value are equal to the spectral radius is determined. Using the -norms for the approximation of the spectral radius of an Hermitian matrix an a priori and a posteriori bounds for the error are obtained. Some properties of the a posteriori bound are discussed.
Correction to "Generalized approximation numbers" (Port. Math., 43(1) (1985-1986), 157-166)