A note on injective envelopes and von Neumann algebras
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2013
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| Soggetti: | |
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| _version_ | 1866929589275590656 |
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| author | Haag, Ulrich |
| author_facet | Haag, Ulrich |
| contents | The article exhibits certain relations between the injective envelope I(A) of a C*-algebra A and the von Neumann algebra generated by a representation lambda of A provided it is injective. More specifically we show that there exist positive retractions sigma : /lambda (A)'' ---> I(A) which are close to being *-homomorphisms in the sense that they are Jordan homomorphisms of the underlying Jordan algebras, and the kernel of /sigma is given by a twosided ideal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1310_3636 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | A note on injective envelopes and von Neumann algebras Haag, Ulrich Operator Algebras 46L07 The article exhibits certain relations between the injective envelope I(A) of a C*-algebra A and the von Neumann algebra generated by a representation lambda of A provided it is injective. More specifically we show that there exist positive retractions sigma : /lambda (A)'' ---> I(A) which are close to being *-homomorphisms in the sense that they are Jordan homomorphisms of the underlying Jordan algebras, and the kernel of /sigma is given by a twosided ideal. |
| title | A note on injective envelopes and von Neumann algebras |
| topic | Operator Algebras 46L07 |
| url | https://arxiv.org/abs/1310.3636 |