Injective envelopes for locally C*-algebras
Operator Algebras
2026-02-04 v2
Abstract
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 Fr\'{e}chet 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 Fr\'{e}chet locally W*-algebras is injective if and only if the C*-algebras from its Arens-Michael decomposition are injective.
Keywords
Cite
@article{arxiv.2502.08608,
title = {Injective envelopes for locally C*-algebras},
author = {Maria Joiţa and Gheorghe-Ionuţ Şimon},
journal= {arXiv preprint arXiv:2502.08608},
year = {2026}
}