Functional Analysis and Applications Seminar 

11/01/2008, 15:00 — 16:00 — Room P3.10, Mathematics Building
Ilya Spitkovsky, College of William and Mary, Williamsburg, Virginia, USA

Spectral dominance and commuting chains

Positive semi-definite (PSD) operator $A$ "spectrally dominates" PSD operator $B$ if $A^t-B^t$ is PSD for all $t \gt 0$. We (i) give a new characterization of spectral dominance in finite dimensions in terms of a monotonic chain of intermediate, pairwise commuting operators and (ii) determine for which pairs $(A;B)$ spectral dominance persists under the taking of arbitrary compressions. Earlier results about spectral dominance are proven (in finite dimensions) in new ways, and several corollary observations are made. This is a joint work with Charlie Johnson and Bich Hoai, accepted for publication by Proceedings of the AMS (and is accessible for students).