Advanced Functional Analysis

Syllabus:
(i) Spectral measure for bounded normal operators and measurable functional calculus.
(ii) von Neumann algebras (double commutant theorem, comparison of projections and 
type classification of von Neumann algebras)
(iii)  Completely positive maps, Stinespring's representation theorem, 
Choi-Kraus representation of  quantum channels and quantum dynamics.

Suggested books:  
(i) V S Sunder, Operators on Hilbert space.
(ii) John B Conway, A course in Operator Theory,
(iii) G J Murphy, C*-algebras and Operator theory.

https://www.isibang.ac.in/~adean/infsys/database/MMath/AFA.html