2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73949Using ideas of S. Wassermann on non-exact $C^*$-algebras and property T groups, we show that one of his examples of non-invertible C*-extensions is not semi-invertible. To prove this, we show that a certain element vanishes in the asymptotic tensor product. We also show that a modification of the example gives a C*-extension which is not even invertible up to homotopy.11 pagesOperator Algebras46L05text