Faithful states on a C^∗-algebra

Masamichi Takesaki

Vol. 52 (1974), No. 2, 605–610

DOI: 10.2140/pjm.1974.52.605

Abstract

Let A be a separable C^∗-algebra which is σ-weakly dense in a von Neumann algebra −ℳ. The equivalence of the following two statements is proven: (i) ℳ is atomic and A contains all miminal projections; (ii) A normal state φ of ℳ is faithful if the restriction φ|_A of φ to A is also.

Mathematical Subject Classification 2000

Primary: 46L05

Milestones

Received: 16 October 1972

Published: 1 June 1974