Classes of conditional expectations over von Neumann algebras

Carlo Cecchini, D. Petz

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

Let N ⊂ M be von Neumann algebras and Eω: M → N an ω-conditional expectation mapping. For a state ψ of N an extension \ ̃gyEω of ψ with respect to Eω is described. The relation Eω ~ Eθ{symbol} defined to hold if \ ̃gyEω = \ ̃gyEθ{symbol} for every ψ is an equivalence relation. The family of equivalence classes possesses an affine structure and shows analogy with the normal state space of a von Neumann algebra.

Original languageEnglish
Pages (from-to)8-29
Number of pages22
JournalJournal of Functional Analysis
Volume92
Issue number1
DOIs
Publication statusPublished - 1990

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Conditional Expectation
Von Neumann Algebra
Affine Structure
Normal Space
Equivalence relation
Equivalence class
Analogy
State Space
Class
Family

ASJC Scopus subject areas

  • Analysis

Cite this

Classes of conditional expectations over von Neumann algebras. / Cecchini, Carlo; Petz, D.

In: Journal of Functional Analysis, Vol. 92, No. 1, 1990, p. 8-29.

Research output: Contribution to journalArticle

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