Conditional Expectations onto Maximal Abelian *-subalgebras
نویسنده
چکیده
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.
منابع مشابه
C*-algebras on r-discrete Abelian Groupoids
We study certain function algebras and their operator algebra completions on r-discrete abelian groupoids, the corresponding conditional expectations, maximal abelian subalgebras (masa) and eigen-functionals. We give a semidirect product decomposition for an abelian groupoid. This is done through a matched pair and leads to a C*-diagonal (for a special case). We use this decomposition to study ...
متن کامل4 Intersections of finite families of finite index
We prove that finiteness of the index of the intersection of a finite set of finite index subalgebras in a von Neumann algebra (with small centre) is equivalent to the finite dimensionality of the algebra generated by the conditional expectations onto the subalgebras. 2000 Mathematics Subject Classification. 46S99, 81R10.
متن کاملMaximal Abelian Subalgebras of O N
We consider maximal abelian subalgebras of O n which are invariant to the standard circle action. It turns out that these are all contained in the zero grade of O n. Then we consider shift invariant maximal abelian subalgebras of the zero grade, which are also invariant to a " second shift " map, and show that these are just infinite tensor products of diagonal matrices in the standard UHF pict...
متن کاملComputing abelian subalgebras for linear algebras of upper-triangular matrices from an algorithmic perspective
In this paper, the maximal abelian dimension is algorithmically and computationally studied for the Lie algebra hn, of n×n upper-triangular matrices. More concretely, we define an algorithm to compute abelian subalgebras of hn besides programming its implementation with the symbolic computation package MAPLE. The algorithm returns a maximal abelian subalgebra of hn and, hence, its maximal abeli...
متن کامل1 6 Ju n 20 04 Intersections of finite families of finite index
We prove that finiteness of the index of the intersection of a finite set of finite index subalgebras in a von Neumann algebra (with small centre) is equivalent to the finite dimensionality of the algebra generated by the conditional expectations onto the subalgebras. Supported in part by NSF gramt DMS-9322675 and Marsden grant UOA520. Supported in part by NSF grant DMS-0200770.
متن کامل