Entrywise positivity preservers in fixed dimension: II

Abstract: The second talk in this series will (after a quick introduction) focus on how to resolve the outstanding questions from the first talk, using additional tools from symmetric function theory and type A representation theory. These tools help extend prior results from entrywise polynomial preservers to finite and infinite sums of real powers, acting on positive matrices with positive entries. We conclude with a novel characterization of weak majorization of real tuples, via Schur polynomials and Vandermonde determinants, and use it to strengthen and extend the Cuttler–Greene–Skandera/Sra characterization of majorization to all real tuples.

(Based on two papers: with Alexander Belton, Dominique Guillot, and Mihai Putinar, Adv. Math. 2016; and with Terence Tao, Amer. J. Math., in press.)

functional analysis

Audience: researchers in the topic

Functional Analysis and Operator Theory Webinar

Series comments: The aim of this lecture series is to provide the community with an opportunity for regular online meetings these days when physical seminars and conferences are not possible.

This seminar is a continuation of the Preserver Webinar series with an intention to widen its scope and range of speakers. If you are interested in following the updates, please write an e-mail to faot[dot]webinar[at]gmail[dot]com with the subject "Subscribe".