Learning Seminar: Takesaki’s noncommutative Gelfand duality (part I)

In this talk, we will start going over Takesaki’s annals paper that proves that every separable C*-algebra A can be represented as continuous “noncommutative” functions with values in B(H) (H separable) on the space of representations of A on H. Furthermore, the universal enveloping von Neumann algebra of A is identified with all the bounded “noncommutative” functions on the same space