Injective envelopes for locally C*-algebras
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914304218890240 |
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| author | Joiţa, Maria Şimon, Gheorghe-Ionuţ |
| author_facet | Joiţa, Maria Şimon, Gheorghe-Ionuţ |
| contents | We introduce the notion of admissible injective envelope for a locally C*-algebra and show that each object in the category whose objects are unital Fréchet locally C*-algebras and whose morphisms are unital admissible local completely positive maps has a unique admissible injective envelope. The concept of admissible injectivity is stronger than that of injectivity. As a consequence, we show that a unital Fréchet locally W*-algebras is injective if and only if the C*-algebras from its Arens-Michael decomposition are injective. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08608 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Injective envelopes for locally C*-algebras Joiţa, Maria Şimon, Gheorghe-Ionuţ Operator Algebras 47L05: 47L25, 46M10, 46A22 We introduce the notion of admissible injective envelope for a locally C*-algebra and show that each object in the category whose objects are unital Fréchet locally C*-algebras and whose morphisms are unital admissible local completely positive maps has a unique admissible injective envelope. The concept of admissible injectivity is stronger than that of injectivity. As a consequence, we show that a unital Fréchet locally W*-algebras is injective if and only if the C*-algebras from its Arens-Michael decomposition are injective. |
| title | Injective envelopes for locally C*-algebras |
| topic | Operator Algebras 47L05: 47L25, 46M10, 46A22 |
| url | https://arxiv.org/abs/2502.08608 |