Analysis Seminar

Laurent Marcoux, Department of Pure Mathematics, University of Waterloo

"Hilbert space operators with compatible off-diagonal corners"

Given a complex, separable Hilbert space $\mathcal{H}$, we characterize those operators for which $\| P T (I − P ) \| = \| (I − P )T P \|$  for all orthogonal projections $P$ on $\mathcal{H}$. 

We also obtain a complete characterization of those operators acting on finite-dimensional Hilbert spaces for which $rank  (I − P )T P = rank P T (I − P )$ for all orthogonal projections $P$, and we discuss extensions of this result to operators acting on infinite dimensional spaces.

This is joint work with L. Livshits (Colby College) G. MacDonald (UPEI), and H. Radjavi (U Waterloo)

MC 5417