Quaternions and Functional Calculus

Quaternions and Functional Calculus

In this paper, we develop the notion of generalized characters and a corresponding Gelfand theory for quaternionic <inline-formula> <math display="inline"> <semantics> <msup> <mi>C</mi> <mo>*</mo> </msup> </semantics> </math>...

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Bibliographic Details
Main Authors: Elham Ghamari, Dan Kučerovský
Format: Article
Language:English
Published: MDPI AG 2019-07-01
Series:Symmetry
Subjects:
quaternions
hilbert space
functional calculus
gelfand theorem
C*-algebras
Online Access:https://www.mdpi.com/2073-8994/11/8/953
Description
Summary:In this paper, we develop the notion of generalized characters and a corresponding Gelfand theory for quaternionic <inline-formula> <math display="inline"> <semantics> <msup> <mi>C</mi> <mo>*</mo> </msup> </semantics> </math> </inline-formula>-algebras. These are C*-algebras whose structure permits an action of the quaternions. Applications are made to functional calculus, and we develop an S-functional calculus related to what we term structural regular functions.
ISSN:2073-8994

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