Tracially sequentially-split ${}^*$-homomorphisms between $C^*$-algebras II

Hyun Ho Lee; Hiroyuki Osaka

Tracially sequentially-split ${}^$-homomorphisms between $C^$-algebras II

Operator Algebras 2022-07-06 v5 Functional Analysis

Authors: Hyun Ho Lee , Hiroyuki Osaka

Abstract

We study a pair of $C^*$ -algebras by associating a $*$ -homomorphism from $A$ to $B$ allowing an approximate left-inverse to the sequence algebra of $A$ in a manner reminiscent of several tracial approximation properties. We are particularly interested how regularity properties in the Elliott classification program pass from $B$ to $A$ . Among them, we show that the strict comparison property and $\mathcal{Z}$ -stability pass from $B$ to $A$ in our setting.

Keywords

c*-algebras hilbert modules c*-algebra

Cite

@article{arxiv.1906.06950,
  title  = {Tracially sequentially-split ${}^*$-homomorphisms between $C^*$-algebras II},
  author = {Hyun Ho Lee and Hiroyuki Osaka},
  journal= {arXiv preprint arXiv:1906.06950},
  year   = {2022}
}

Comments

This is a finalized version. It will appear in J. Topology and Analysis. 16 pages