2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/157972Let X be a Hilbert bimodule over a C*-algebra A and $O_X= A \rtimes_X \Z$. Using a finite section method we construct a sequence of completely positive contractions factoring through matrix algebras over A which act on $s_ξ s_η^*$ as Schur multipliers converging to the identity. This shows immediately that for a finitely generated X the algebra $O_X$ inherits any standard approximation property such as nuclearity, exactness, CBAP or OAP from A. We generalise this to certain general Pimsner algebras by proving semi-splitness of the Toeplitz extension under certain conditions and discuss some examples.11 pages, v2 has a modified title, abstract and introduction. The paper will appear in the Rocky Mountain Journal of MathematicsOperator AlgebrasFunctional AnalysisPrimary 46L05, Secondary 46B28text