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Publication Detailed Description
Journal Title
Proceedings of the Edinburgh Mathematical Society
Year (definitive publication)
2024
Language
English
Country
United Kingdom
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Abstract
The numerical range in the quaternionic setting is, in general, a non-convex subset of the quaternions. The essential numerical range is a refinement of the numerical range that only keeps the elements that have, in a certain sense, infinite multiplicity. We prove that the essential numerical range of a bounded linear operator on a quaternionic Hilbert space is convex. A quaternionic analogue of Lancaster theorem, relating the closure of the numerical range and its essential numerical range, is also provided.
Acknowledgements
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Keywords
Quaternions,Numerical range,Essential numerical range
Fields of Science and Technology Classification
- Mathematics - Natural Sciences
Funding Records
| Funding Reference | Funding Entity |
|---|---|
| UIDB/04459/2020 | Fundação para a Ciência e a Tecnologia |
| UIDB/04674/2020 | Fundação para a Ciência e a Tecnologia |
| UIDB/00212/2020 | Fundação para a Ciência e a Tecnologia |
| UIDP/04459/2020 | Fundação para a Ciência e a Tecnologia |
