Algebraic equivalence of locally normal representations

Masamichi Takesaki

Vol. 34 (1970), No. 3, 807–816

DOI: 10.2140/pjm.1970.34.807

Abstract

It will be shown that (i) the absolute value of every locally normal linear functional is again locally normal; (ii) two locally normal representations π₁ and π₂ of 𝒜 generate isomorphic von Neumann algebras ℳ(π₁) and ℳ(π₂) if and only if there exists an automorphism σ of 𝒜 such that π₁ ∘ σ and π₂ are quasi-equivalent, provided that either ℳ(π₁) or ℳ(π₂) is σ-finite.

Mathematical Subject Classification

Primary: 46.65

Milestones

Received: 22 January 1970

Published: 1 September 1970