CONDITIONAL EXPECTATIONS ONTO MAXIMAL ABELIAN -SUBALGEBRAS

CONDITIONAL EXPECTATIONS ONTO MAXIMAL ABELIAN -SUBALGEBRAS

We determine when there is a unique conditional expectation from a semifinite von Neumann algebra onto a singly-generated maximal abelian *-subalgebra. Our work extends the results of Kadison and Singer via new methods, notably the observation that a unique conditional expectation onto a singly-gene...

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Bibliographic Details
Published in:Journal of operator theory Vol. 68; no. 2; pp. 597 - 607
Main Authors: AKEMANN, CHARLES A., SHERMAN, DAVID
Format: Journal Article
Language:English
Published: Theta Foundation 01-10-2012
Subjects:
Algebra
Fourier analysis
Index sets
Mathematical theorems
Operator algebras
Operator theory
Subalgebras
Uniqueness
Von Neumann algebra
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Summary:We determine when there is a unique conditional expectation from a semifinite von Neumann algebra onto a singly-generated maximal abelian *-subalgebra. Our work extends the results of Kadison and Singer via new methods, notably the observation that a unique conditional expectation onto a singly-generated maximal abelian *-subalgebra must be normal.
ISSN:0379-4024
1841-7744