2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67180In a wide class of weighted Bergman spaces, we construct invertible non-cyclic elements. These are then used to produce z-invariant subspaces of index higher than one. In addition, these elements generate nontrivial bilaterally invariant subspaces in anti-symmetrically weighted Hilbert spaces of sequences.40 pagesFunctional AnalysisComplex Variables30H05, 47A15, 30D99, 42A65, 43A15, 46E20, 46J15text