Some results and questions around multivariate majorization

Leonel Robert González  (University of Louisiana at Lafayette)

10:00-11:00, July 7, 2020   Zoom 514 693 6752


Given n-tuples of real numbers v and w, v is said to be majorized by w if there exists a double stochastic matrix D such that v = Dw. (Another well known characterization of majorization is in terms of a collection of inequalities.) If v and w are the eigenvalues of selfadjoint matrices V and W, then v majorized by w means that matrix V is a convex combination of unitary conjugates of W. These classical results have natural generalizations to the C*-algebra setting. Multivariate/simultaneous majorization comes about when one considers collections of vectors (v_1,v_2,...,v_m) and (w_1,w_2,...,w_m) and asks that v_i = Dw_i for a doubly stochastic D and all i. This complicates things both in the finite dimensional set-up of vectors and matrices, as well as in the C*-algebraic one. I will discuss a number of results and questions around this concept.

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