标题： 局部C*-代数的内射包络 显示英文标题

标题： Injective envelopes for locally C*-algebras

摘要： 我们引入了局部C*-代数的可接受内射包的概念，并证明在对象为单位Fréchet局部C*-代数、态射为单位可接受局部完全正映射的范畴中，每个对象都有唯一的可接受内射包。 可接受内射性的概念比内射性更强。 作为结果，我们证明一个单位Fréchet局部W*-代数是内射的当且仅当其Arens-Michael分解中的C*-代数是内射的。 显示英文摘要

摘要： 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.