Vol. 27, No. 2, 1968

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Normal expectations in von Neumann algebras

André (Piotrowsky) De Korvin

Vol. 27 (1968), No. 2, 333–338

Let h and k be two Hilbert spaces, h k will denote the tensor product of h and k. Let 𝒜 be a von Neumann algebra acting on h. Let ψ be an ampliation of 𝒜 in h k, i.e., ψ is a map of 𝒜 into bounded linear operators of h k and ψ(𝒜) = 𝒜⊗ Ik (Ik is the identity map on k). Let 𝒜 be the image of 𝒜 by ψ.

The purpose of this paper is to prove the following result: If is a subalgebra of 𝒜 and if is the range of a normal expectation φ defined on 𝒜, then there exists an ampliation of 𝒜 in h k, independent of and of φ, such that φ Ik is a spatial isomorphism of 𝒜.

Mathematical Subject Classification
Primary: 46.65
Received: 13 November 1967
Published: 1 November 1968
André (Piotrowsky) De Korvin