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- W1666176186 abstract "We introduce the concept of a direct $C_{omega}^{ast}$-system and show that every non-separable unital $C^{ast}$-algebra is the limit of essentially unique direct $C_{omega}^{ast}$-system. This result is then applied to the problem of characterization of projective unital $C^{ast}$-algebras. It is shown that a non-separable unital $C^{ast}$-algebra $X$ of density $tau$ is projective if and only if it is the limit of a well ordered direct system ${mathcal S}_{X} = {X_{alpha}, i_{alpha}^{alpha +1}, alpha f>> Y @A{p}AA @AA{q}A X_{0} @>f_{0}>> Y_{0}, end{CD} ] noindent where $X_{0}$ and $Y_{0}$ are separable unital projective $C^{ast}$-algebras and the homomorphisms $i_{0} colon X_{0} to Y_{0}$, $p colon X_{0} to X$ and $q colon Y_{0} to Y$ are doubly projective. These two results provide a complete characterization of non-separable projective unital $C^{ast}$-algebras in terms of separable ones." @default.
- W1666176186 created "2016-06-24" @default.
- W1666176186 creator A5041376194 @default.
- W1666176186 date "1999-08-15" @default.
- W1666176186 modified "2023-09-27" @default.
- W1666176186 title "Uncountable direct systems and a characterization of non-separable projective $C^{ast}$-algebras" @default.
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