2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/114143We study the relative position of four subspaces in a Hilbert space. For any positive integer n, we give an example of exotic indecomposable system of four subspaces in a Hilbert space whose defect is (2n+1)/3. By an exotic system, we mean a system which is not isomorphic to any closed operator system under any permutation of subspaces. We construct the examples by a help of certain nice sequences used by Jiang and Wang in their study of strongly irreducible operators.16pagesFunctional AnalysisOperator Algebras46C05, 47A15text