2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/133078We study indecomposable representations of quivers on separable infinite-dimensional Hilbert spaces by bounded operators. We consider a complement of Gabriel's theorem for these representations. Let $Γ$ be a finite, connected quiver. If its underlying undirected graph contains one of extended Dynkin diagrams $\tilde{A_n} (n \geq 0)$, $\tilde{D_n} (n \geq 4)$, $\tilde{E_6}$,$\tilde{E_7}$ and $\tilde{E_8}$, then there exists an indecomposable representation of $Γ$ on separable infinite-dimensional Hilbert spaces.34 pagesOperator AlgebrasRepresentation Theory46C07, 47A15, 15A21, 16G20, 16G60text