The carpenter and Schur--Horn problems for masas in finite factors

Details The carpenter and Schur--Horn problems for masas in finite factors The carpenter and Schur--Horn problems for masas in finite factors

2011-10-29

arxiv.org/abs/1110.6500v1

Mathematics

Operator Algebras

15 pages

Scientific paper

Two classical theorems in matrix theory, due to Schur and Horn, relate the eigenvalues of a self-adjoint matrix to the diagonal entries. These have recently been given a formulation in the setting of operator algebras as the Schur-Horn problem, where matrix algebras and diagonals are replaced respectively by finite factors and maximal abelian self-adjoint subalgebras (masas). There is a special case of the problem, called the carpenter problem, which can be stated as follows: for a masa A in a finite factor M with conditional expectation E_A, can each x in A with 0 <= x <= 1 be expressed as E_A(p) for a projection p in M? In this paper, we investigate these problems for various masas. We give positive solutions for the generator and radial masas in free group factors, and we also solve affirmatively a weaker form of the Schur-Horm problem for the Cartan masa in the hyperfinite factor.

Affiliated with

Also associated with

No associations

Rating

The carpenter and Schur--Horn problems for masas in finite factors does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The carpenter and Schur--Horn problems for masas in finite factors, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The carpenter and Schur--Horn problems for masas in finite factors will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-200191