Kantarovich-type inequalities for operators via D-optimal design theory
Luc Pronzato, Henry Wynn and Anatoly Zhigljavsky
Linear Algebra and its Applications Volume 410, pp. 160-169, 2005.

Abstract

The Katarovich inequality is $z^TAzz^TA^{-1}z\le (M+m)^2/(4mM)$, where $A$ is a positive definite symmetric operator in R^d, z is a unit vector and m and M are respectively the smallest and largest eigenvalues of A. This is generalised both for operators in R^d and in Hilbert space by noting a connection with D-optimal design theory in mathematical statistics. Each geenralised bound is found as the maxima of the determinant of a suitable moment matrix.

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