Renault's $j$-map for Fell bundle $C^*$-algebras

Anna Duwenig; Dana P. Williams; Joel Zimmerman

Renault's $j$-map for Fell bundle $C^*$-algebras

Operator Algebras 2022-03-03 v1

Authors: Anna Duwenig , Dana P. Williams , Joel Zimmerman

Abstract

If $p \colon \mathcal B\to G$ is a Fell bundle over an \'etale groupoid, then we show that there is an norm reducing injective linear map $j \colon C^*_r(G;\mathcal B)\to \Gamma_{0}(G;\mathcal B)$ generalizing the well know map $j \colon C^*_{r}(G)\to C_{0}(G)$ in the case of an \'etale groupoid.

Cite

@article{arxiv.2203.01165,
  title  = {Renault's $j$-map for Fell bundle $C^*$-algebras},
  author = {Anna Duwenig and Dana P. Williams and Joel Zimmerman},
  journal= {arXiv preprint arXiv:2203.01165},
  year   = {2022}
}

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