On $\ell$-open $C^{\ast }$ algebras and $\ell$-closed $C^{\ast }$-algebras

Abstract

In this paper, we characterize $\ell$-open and $\ell$-closed $C^{\ast }$-algebras and deduce that $\ell$-open $C^{\ast }$-algebras are $\ell$-closed, as conjectured by Blackadar. Moreover, we show that a commutative unital $C^{\ast }$-algebra is $\ell$-open if and only if it is semiprojective.

arXiv commentMinor changes. Added Remark 4.4 and Proposition 5.3