Weakly Stable Relations and Inductive Limits of $C^ast$-algebras

[摘要] We show that if $mathcal{A}$ is a class of $C^ast$-algebras for whichthe set of formal relations $mathcal{R}$ is weakly stable, then $mathcal{R}$is weakly stable for the class $mathcal{B}$ that contains $mathcal{A}$ andall the inductive limits that can be constructed with the $C^ast$-algebras in$mathcal{A}$.A set of formal relations $mathcal{R}$ is said to be {it weakly stable/} fora class $mathcal{C}$ of $C^ast$-algebras if, in any $C^ast$-algebra $Ainmathcal{C}$, close to an approximate representation of the set $mathcal{R}$in $A$ there is an exact representation of $mathcal{R}$ in $A$.

[学科分类] 数学（综合）