S-spectrum and numerical range of a quaternionic operator

2022/10/11 by Luís Carvalho, Carvalho, Luís, Cristina Diogo +3
Computer Science · Mathematics · #15B33 #47A12 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2210.05535

openalex publication_date 2022/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the numerical range of bounded linear operators on quaternionic Hilbert spaces and its relation with the S-spectrum. The class of complex operators on quaternionic Hilbert spaces is introduced and the upper bild of normal complex operators is completely characterized in this setting.

Related

• Normal operators in real and quaternionic Hilbert spaces
• Decomposable operators, local S-spectrum and S-spectrum in the quaternionic setting
• A new approach to the S-functional calculus
• Quaternionic numerical range of complex matrices
• Perturbation of normal quaternionic operators