2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63431Let H be a separable, infinite dimensional Hilbert space and let S be a countable subset of H. Then most positive operators on H have the property that every nonzero vector in the span of S is cyclic, in the sense that the set of operators in the positive part of the unit ball of B(H) with this property is comeager for the strong operator topology. Suppose κis a regular cardinal such that κ\geq ω_1 and 2^{<κ} = κ. Then it is relatively consistent with ZFC that 2^ω= κand for any subset S \subset H of cardinality less than κthe set of positive operators in the unit ball of B(H) for which every nonzero vector in the span of S is cyclic is comeager for the strong operator topology.6 pagesFunctional AnalysisLogic03E35, 03E50, 47A15, 47A16text