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.
Books
John B. Conway, A course in Functional Analysis, Springer, 1985.
Vern Paulson., Completely Bounded Maps and
Dilations, Pitman Research Notes, 1986.