1. Hilbert space operators with compatible off-diagonal corners
- Author
-
Livshits, L., MacDonald, G., Marcoux, L. W., and Radjavi, H.
- Subjects
Mathematics - Functional Analysis ,15A60, 47A20, 47A30, 47B15 - Abstract
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 $\mathcal{H}$. When $\mathcal{H}$ is finite-dimensional, we also obtain a complete characterization of those operators for which $\mathrm{rank}\, (I-P) T P = \mathrm{rank}\, P T (I-P)$ for all orthogonal projections $P$. When $\mathcal{H}$ is infinite-dimensional, we show that any operator with the latter property is normal, and its spectrum is contained in either a line or a circle in the complex plane., Comment: 24 pages
- Published
- 2017