Injective envelopes for locally C*-algebras

Fuente: arXiv
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Hauptverfasser: Joiţa, Maria, Şimon, Gheorghe-Ionuţ
Format: Preprint
Veröffentlicht: 2025
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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