Injective envelopes of real C*- and AW*-algebras
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913683797442560 |
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| author | Rakhimov, A. A. Ramazonova, L. D. |
| author_facet | Rakhimov, A. A. Ramazonova, L. D. |
| contents | It is shown that every outer *-automorphism of a real C*-algebra can be uniquely extended to an injective envelope of real C*-algebra. It is proven that if a real C*-algebra is a simple, then its injective envelope is also simple, and it is a real AW*-factor. The example of a real C*-algebra that is not real AW*-algebra and the injective envelope is a real AW*-factor of type III, which is not a real W*-algebra is constructed. This leads to the interesting result that up to isomorphism, the class of injective real (resp. complex) AW*-factors of type III is at least one larger than the class injective real (resp. complex) W*-factors of type III. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_04137 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Injective envelopes of real C*- and AW*-algebras Rakhimov, A. A. Ramazonova, L. D. Operator Algebras 46L35, 46L10, 47L30, 47L40 It is shown that every outer *-automorphism of a real C*-algebra can be uniquely extended to an injective envelope of real C*-algebra. It is proven that if a real C*-algebra is a simple, then its injective envelope is also simple, and it is a real AW*-factor. The example of a real C*-algebra that is not real AW*-algebra and the injective envelope is a real AW*-factor of type III, which is not a real W*-algebra is constructed. This leads to the interesting result that up to isomorphism, the class of injective real (resp. complex) AW*-factors of type III is at least one larger than the class injective real (resp. complex) W*-factors of type III. |
| title | Injective envelopes of real C*- and AW*-algebras |
| topic | Operator Algebras 46L35, 46L10, 47L30, 47L40 |
| url | https://arxiv.org/abs/2502.04137 |