Scientific journal paper Q1
On the convexity of the quaternionic essential numerical range
Luís Carvalho (Carvalho, L.); Cristina Diogo (Diogo, C.); Sérgio Mendes (Mendes, S.); Helena Soares (Soares, H.);
Journal Title
Proceedings of the Edinburgh Mathematical Society
Year (definitive publication)
N/A
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
Publication Identifiers
ci-pub-104133
2-s2.0-85193854496
WOS:001223238800001
10.1017/S0013091524000336
http://hdl.handle.net/10071/31747
Other Publication Details
2024
Cambridge University Press
Web of Science©; Scopus;
0013-0915 (print)
1464-3839 (online)
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Yes
Link to the repository
2024-05-15
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