On $\ell$-open $C^*$ algebras and $\ell$-closed $C^*$-algebras

Dolapo Oyetunbi; Aaron Tikuisis

On $\ell$-open $C^$ algebras and $\ell$-closed $C^$-algebras

Operator Algebras 2024-01-31 v2

Authors: Dolapo Oyetunbi , Aaron Tikuisis

Abstract

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

Keywords

C*-algebras l-open l-closed semiprojective commutative unital

Cite

@article{arxiv.2310.15155,
  title  = {On $\ell$-open $C^*$ algebras and $\ell$-closed $C^*$-algebras},
  author = {Dolapo Oyetunbi and Aaron Tikuisis},
  journal= {arXiv preprint arXiv:2310.15155},
  year   = {2024}
}

Comments

Minor changes. Added Remark 4.4 and Proposition 5.3

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