Premise: In mathematics, an O*-algebra is an algebra of possibly unbounded operators defined on a dense subspace of a Hilbert space. The original examples were described by and , who studied some examples of O*-algebras, called Borchers algebras, arising from the Wightman axioms of quantum field theory. and began the systematic study of algebras of unbounded operators.
Hypothesis: Hilbert spaces only have non-dense subspaces