Set theory and cyclic vectors
N Weaver�- Journal of Operator Theory, 2004 - JSTOR
N Weaver
Journal of Operator Theory, 2004•JSTORLet 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 κ is a regular
cardinal such that κ≥ ω1 and 2< κ= κ. Then it is relatively consistent with ZFC that 2ω= κ and
for any subset S⊂ H of cardinality less than κ the set of positive operators in the unit ball of B�…
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 κ is a regular
cardinal such that κ≥ ω1 and 2< κ= κ. Then it is relatively consistent with ZFC that 2ω= κ and
for any subset S⊂ H of cardinality less than κ the set of positive operators in the unit ball of B�…
Let 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 κ is a regular cardinal such that κ ≥ ω1 and 2<κ = κ. Then it is relatively consistent with ZFC that 2ω = κ and for any subset S ⊂ H of cardinality less than κ the 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.
JSTOR