Spectrum and analytic functional calculus ...
Document type :
Compte-rendu et recension critique d'ouvrage
DOI :
Title :
Spectrum and analytic functional calculus in real and quaternionicframeworks: An overview
Author(s) :
Journal title :
AIMS Mathematics
Publisher :
AIMS Press
Publication date :
2023-12-22
English keyword(s) :
spectrum in real algebras
conjugation
real operators
quaternionic operators
analytic functional calculus
conjugation
real operators
quaternionic operators
analytic functional calculus
HAL domain(s) :
Mathématiques [math]
English abstract : [en]
An approach to the elementary spectral theory for quaternionic linear operators waspresented by the author in a recent paper, quoted and discussed in the Introduction, where, unlikein works by other authors, the construction ...
Show more >An approach to the elementary spectral theory for quaternionic linear operators waspresented by the author in a recent paper, quoted and discussed in the Introduction, where, unlikein works by other authors, the construction of the analytic functional calculus used a Riesz-Dunford-Gelfand type kernel, and the spectra were defined in the complex plane. In fact, the present authorregards the quaternionic linear operators as a special class of real linear operators, a point of viewleading to a simpler and a more natural approach to them. The author’s main results in this frameworkare summarized in the following, and other pertinent comments and remarks are also included in thistext. In addition, a quaternionic joint spectrum for pairs of operators is discussed, and an analyticfunctional calculus which uses a Martinelli type kernel in two variables is recalled.Show less >
Show more >An approach to the elementary spectral theory for quaternionic linear operators waspresented by the author in a recent paper, quoted and discussed in the Introduction, where, unlikein works by other authors, the construction of the analytic functional calculus used a Riesz-Dunford-Gelfand type kernel, and the spectra were defined in the complex plane. In fact, the present authorregards the quaternionic linear operators as a special class of real linear operators, a point of viewleading to a simpler and a more natural approach to them. The author’s main results in this frameworkare summarized in the following, and other pertinent comments and remarks are also included in thistext. In addition, a quaternionic joint spectrum for pairs of operators is discussed, and an analyticfunctional calculus which uses a Martinelli type kernel in two variables is recalled.Show less >
Language :
Anglais
Popular science :
Non
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