Fourth Edition of the International Conference on Research in Applied Mathematics and Computer Science ICRAMCS 2022
 March 24-25-26, 2022
Online and Face-to-Face Conference

ICRAMCS, 4 (2022) | Proceedings ISSN: 2605-7700

Research Communication | Open Access
Volume 2022 | Communication ID 228
Numerical range of quaternionic right linear bounded operators
Somayya Moulaharabbi, Mohamed Barraa, El Hassan Benabdi
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
January 27, 2022
March 03, 2200
April 15, 2200

Abstract: In this paper, we prove that for a right linear bounded operator on a quaternionic Hilbert space, the norm and the numerical radius are equal if and only if the norm and the spectral radius are equal.Wealso show that the spherical spectrum of a quaternionic bounded operator is included in the closure of its numerical range, and we show that the numerical range of an operator on a quaternionic Hilbert space is not necessarily convex. For a quaternionic bounded normal operator, weprove that the convex hull of the closure of its numerical range is equal to the convex hull of its ...