Faithful states on aC∗-algebra
Masamichi Takesaki · Pacific Journal of Mathematics · 1974
Let A be a separable C*-algebra which is σ-weakly dense in a von Neumann algebra ~-*C The equivalence of the following two statements is proven: (i) ^ is atomic and A contains all miminal projections; (ii) A normal state φ of ^ is faithful if the restriction ψ\ A of φ to A is also.