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| Main Author: | |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2103.16266 |
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| _version_ | 1866911076118953984 |
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| author | Vasilescu, Florian-Horia |
| author_facet | Vasilescu, Florian-Horia |
| contents | A new approach to normal operators in real Hilbert spaces is discussed, and a spectral representation is obtained, derived directly from the complex case. The results are then applied to quaternionic normal operators, regarded as a special class of real normal operators. This point of view allows us to consider their spectrum and associated measures to be defined on subsets of the complex plane, in a classical manner. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_16266 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Normal operators in real and quaternionic Hilbert spaces Vasilescu, Florian-Horia Functional Analysis Subject Classification 2020: 47B15, 47A60, 47S05 A new approach to normal operators in real Hilbert spaces is discussed, and a spectral representation is obtained, derived directly from the complex case. The results are then applied to quaternionic normal operators, regarded as a special class of real normal operators. This point of view allows us to consider their spectrum and associated measures to be defined on subsets of the complex plane, in a classical manner. |
| title | Normal operators in real and quaternionic Hilbert spaces |
| topic | Functional Analysis Subject Classification 2020: 47B15, 47A60, 47S05 |
| url | https://arxiv.org/abs/2103.16266 |