11/01/2008, 15:00 — 16:00 — Sala P3.10, Pavilhão de Matemática
Ilya Spitkovsky, College of William and Mary, Williamsburg, Virginia, USA
Spectral dominance and commuting chains
Positive semi-definite (PSD) operator "spectrally dominates"
PSD operator if is PSD for all . 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 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).