State extensions and a Radon-Nikodym theorem for conditional expectations on Von Neumann algebras

Carlo Cecchini, D. Petz

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10 Citations (Scopus)

Abstract

Let M be a von Neumann algebra with a von Neumann subalgebra M0. If E is a conditional expectation (i.e., projection of norm one) from M into M0, then any faithful normal state φ0 admits a natural extension φ0 {ring-operator} E with respect to E in the sense that E = Eφ0·E• If Eω is only an ω-conditional expectation, then φ0 {ring-operator} Eω is not always an extension of φ0. This paper is devoted to the construction of an extension φ0 of φ0 generalizing the above situation for ω-conditional expectations, which leads also to a Radon-Nikodym theorem for ω-conditional expectation under suitable majorization condition.

Original languageEnglish
Pages (from-to)9-24
Number of pages16
JournalPacific Journal of Mathematics
Volume138
Issue number1
Publication statusPublished - 1989

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ASJC Scopus subject areas

  • Mathematics(all)

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