2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62126We study bounded and unbounded representations of the $*$-algebra $Q_{n,λ}(*)$ generated by $n$ idempotents whose sum equals $λe$ ($λ\in{\mathbb C}$, $e$ is the identity).Operator Algebras46K10; 46L05; 47L05On bounded and unbounded idempotents whose sum is a multiple of the identitytext