In search of convexity: diagonals and numerical ranges
Functional Analysis
2021-02-16 v2
Abstract
We show that the set of all possible constant diagonals of a bounded Hilbert space operator is always convex. This, in particular, answers an open question of J.-C. Bourin (). Moreover, we show that the joint numerical range of a commuting operator tuple is in general not convex, which fills a gap in the literature. We also prove that the Asplund-Ptak numerical range (which is convex for pairs of operators) is, in general, not convex for tuples of operators.
Keywords
Cite
@article{arxiv.2010.09129,
title = {In search of convexity: diagonals and numerical ranges},
author = {Vladimir Müller and Yuri Tomilov},
journal= {arXiv preprint arXiv:2010.09129},
year = {2021}
}
Comments
17 pages. This is a version of the paper to appear in Bulletin of the London Mathematical Society