Groupoids and Hermitian Banach *-algebras

Abstract

We study when the twisted groupoid Banach *-algebra [Formula: see text] is Hermitian. In particular, we prove that Hermitian groupoids satisfy the weak containment property. Furthermore, we find that for [Formula: see text] to be Hermitian it is sufficient that [Formula: see text] is Hermitian. Moreover, if [Formula: see text] is ample, we find necessary conditions for [Formula: see text] to be Hermitian in terms of the fibers [Formula: see text].