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

  Published:2003-12-01
 Printed: Dec 2003
  • Martha Salerno Monteiro
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Abstract

We show that if $\mathcal{A}$ is a class of $C^\ast$-algebras for which the set of formal relations $\mathcal{R}$ is weakly stable, then $\mathcal{R}$ is weakly stable for the class $\mathcal{B}$ that contains $\mathcal{A}$ and all 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\/} for a class $\mathcal{C}$ of $C^\ast$-algebras if, in any $C^\ast$-algebra $A\in \mathcal{C}$, close to an approximate representation of the set $\mathcal{R}$ in $A$ there is an exact representation of $\mathcal{R}$ in $A$.
MSC Classifications: 46L05 show english descriptions General theory of $C^*$-algebras 46L05 - General theory of $C^*$-algebras
 

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