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http://hdl.handle.net/10071/31747| Author(s): | Carvalho, L. Diogo, C. Mendes, S. Soares, H. |
| Date: | 2024 |
| Title: | On the convexity of the quaternionic essential numerical range |
| Journal title: | Proceedings of the Edinburgh Mathematical Society |
| Volume: | 67 |
| Number: | 3 |
| Pages: | 838 - 851 |
| Reference: | Carvalho, L., Diogo, C., Mendes, S., & Soares, H. (2024). On the convexity of the quaternionic essential numerical range. Proceedings of the Edinburgh Mathematical Society, 67(3), 838-851. https://doi.org/10.1017/S0013091524000336 |
| ISSN: | 0013-0915 |
| DOI (Digital Object Identifier): | 10.1017/S0013091524000336 |
| Keywords: | Quaternions Numerical range Essential numerical range |
| 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. |
| Peerreviewed: | yes |
| Access type: | Open Access |
| Appears in Collections: | BRU-RI - Artigos em revistas científicas internacionais com arbitragem científica DM-RI - Artigos em revistas científicas internacionais com arbitragem científica |
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| File | Size | Format | |
|---|---|---|---|
| article_104133.pdf | 520,06 kB | Adobe PDF | View/Open |
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