On the convexity of the quaternionic essential numerical range
Functional Analysis
2022-10-12 v1
Abstract
The numerical range in the quaternionic setting is, in general, a non convex subset of the quaternions. The essential numerical range is a refinement of the numerical range that only keeps the elements that have, in a certain sense, infinite multiplicity. We prove that the essential numerical range of a bounded linear operator on a quaternionic Hilbert space is convex. A quaternionic analogue of Lancaster theorem, relating the closure of the numerical range and its essential numerical range, is also provided.
Cite
@article{arxiv.2210.05520,
title = {On the convexity of the quaternionic essential numerical range},
author = {Luís Carvalho and Cristina Diogo and Sérgio Mendes and Helena Soares},
journal= {arXiv preprint arXiv:2210.05520},
year = {2022}
}