Sz.-Nagy Foias theory: Dilation of contractions on a Hilbert space, minimal isometric dilation, unitary dilation. Von Neumann’s inequality.
Ando’s theorem: simultaneous dilation of a pair of commuting contractions. Parrott’s example of a triple of contractions which cannot be dilated simultaneously. Creation operators on the full Fock space and the symmetric Fock space.
Operators spaces. Completely positive and completely bounded maps. Endomorphisms. Towards dilation of completely positive maps. Unbounded operators: Basic theory of unbounded self-adjoint operators.