Vol. 27, No. 2, 1968

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
Normal expectations in von Neumann algebras

André (Piotrowsky) De Korvin

Vol. 27 (1968), No. 2, 333–338
Abstract

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
Milestones
Received: 13 November 1967
Published: 1 November 1968
Authors
André (Piotrowsky) De Korvin