Journal of Operator Theory

Volume 68, Issue 2, Fall 2012 pp. 597-607.

Conditional expectations onto maximal abelian $*$-subalgebras

Authors: Charles A. Akemann (1) and David Sherman (2)
Author institution: (1) Department of Mathematics, University of California, Santa Barbara, CA 93106, U.S.A.
(2) Department of Mathematics, University of Virginia, P.O. Box 400137, Charlottesville, VA 22904, U.S.A.

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.

Keywords: von Neumann algebra, conditional expectation, maximal abelian $*$-subalgebra, Kadison-Singer problem

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