Vol. 52, No. 2, 1974

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ISSN: 0030-8730
Faithful states on a Cāˆ—-algebra

Masamichi Takesaki

Vol. 52 (1974), No. 2, 605ā€“610
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) is atomic and A contains all miminal projections; (ii) A normal state φ of 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
Authors
Masamichi Takesaki