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>...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2019-07-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/11/8/953 |
| _version_ | 1811184958643896320 |
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| author | Elham Ghamari Dan Kučerovský |
| author_facet | Elham Ghamari Dan Kučerovský |
| author_sort | Elham Ghamari |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T13:21:12Z |
| format | Article |
| id | doaj.art-394ae73ca1df4f9aa2e282dcd2ff5dae |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T13:21:12Z |
| publishDate | 2019-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-394ae73ca1df4f9aa2e282dcd2ff5dae2022-12-22T04:22:11ZengMDPI AGSymmetry2073-89942019-07-0111895310.3390/sym11080953sym11080953Quaternions and Functional CalculusElham Ghamari0Dan Kučerovský1Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB E3B 5A3, CanadaDepartment of Mathematics and Statistics, University of New Brunswick, Fredericton, NB E3B 5A3, CanadaIn 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.https://www.mdpi.com/2073-8994/11/8/953quaternionshilbert spacefunctional calculusgelfand theoremC*-algebras |
| spellingShingle | Elham Ghamari Dan Kučerovský Quaternions and Functional Calculus Symmetry quaternions hilbert space functional calculus gelfand theorem C*-algebras |
| title | Quaternions and Functional Calculus |
| title_full | Quaternions and Functional Calculus |
| title_fullStr | Quaternions and Functional Calculus |
| title_full_unstemmed | Quaternions and Functional Calculus |
| title_short | Quaternions and Functional Calculus |
| title_sort | quaternions and functional calculus |
| topic | quaternions hilbert space functional calculus gelfand theorem C*-algebras |
| url | https://www.mdpi.com/2073-8994/11/8/953 |
| work_keys_str_mv | AT elhamghamari quaternionsandfunctionalcalculus AT dankucerovsky quaternionsandfunctionalcalculus |