Local Lidskii's theorems for unitarily invariant norms

NOELIA BELÉN RIOS; DEMETRIO STOJANOFF; PEDRO GUSTAVO MASSEY

Ciudad Autónoma de Buenos Aires

Congreso; Mathematical encounters Analysis/Noncommutative Analysis/Probability-Stochastics/PDEs and Applications - Junior program; 2019

Instituto Argentino de Matemática- CONICET

Lidskii's additive inequalities (both for eigenvalues and singular values) can be interpretedas an explicit description of global minimizers of functions that are built on unitarily invariant norms, withdomains consisting of certain orbits of matrices (under the action of the unitary group). In this talk, we showthat Lidskii's inequalities actually describe all global minimizers of such functions and that local minimizers are also global minimizers. As an application of this result, we show that local minimizers of generalized frame operator distances in the context of finite frame theory are actually global minimizers.