Author(s): Carvalho, L. ; Diogo, C. ; Mendes, S. ; Soares, H.
Date: 2024
Persistent ID: http://hdl.handle.net/10071/31747
Origin: Repositório ISCTE
Subject(s): Quaternions; Numerical range; Essential numerical range
Document details
On the convexity of the quaternionic essential numerical range
Description
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.
Document Type
Journal article
Language English
Language English
