An algebra whose subalgebras are characterized by density

Alessandro Vignati

doi:10.1017/jsl.2014.86

An algebra whose subalgebras are characterized by density

Operator Algebras 2016-03-16 v3

Authors: Alessandro Vignati

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Abstract

We refine a construction of Choi, Farah and Ozawa to build a nonseparable amenable operator algebra $\mathcal A\subseteq\ell_\infty(M_2)$ whose nonseparable subalgebras, including $\mathcal A$ , are not isomorphic to a $C^*$ -algebra. This is done using a Luzin gap and a uniformly bounded group representation. Next, we study additional properties of $\mathcal A$ and of its separable subalgebras, related to the Kadison Kastler metric.

Keywords

c*-algebras associative algebras lie algebras

Cite

@article{arxiv.1402.1112,
  title  = {An algebra whose subalgebras are characterized by density},
  author = {Alessandro Vignati},
  journal= {arXiv preprint arXiv:1402.1112},
  year   = {2016}
}

Comments

Version updated; accepted for publication in Journal of Symbolic logic

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