2022/10/11 by Luís Carvalho, Carvalho, Luís, Cristina Diogo +5
Computer Science · Mathematics · #47A12 #47S05 #Advanced Optimization Algorithms Research #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2210.05520
openalex publication_date 2022/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.