Unbounded Operator Algebras and Representation Theory

a₁ absolutely convex adjoint algebra with unit assume assumption b₁ B₁(A B₁(B B₁(H bounded operator bounded sets bounded subset c₂ closure cofinal converges Corollary D₁ D₂ defined definition denote dense in H domain dU(x element equivalent essentially self-adjoint Example exists F(DA family of seminorms finite Frechet space graph topology Hence hermitian Hilbert space implies involution isomorphism L+(D L+(DA Lemma linear mapping linear subspace locally convex space locally convex topology metrizable Neumann algebra normed space notation numbers O-family O-neighbourhood O*-algebra operator on H polynomial positive linear functional positive sequence projection Proposition prove QF-space Remark resp satisfies SCHMÜDGEN Section self-adjoint operator self-adjoint representation seminorms shows space H Suppose symmetric operator t₁ topological algebra U(exp vector space von Neumann algebra x₁ л₁