Towards the Carpenter's Theorem
Operator Algebras
2011-06-01 v1
Abstract
Let M be a II_1 factor, A a masa in M and E the unique conditional expectation on A. Under some technical assumptions on the inclusion of A in M, which hold true for any semiregular masa of a separable factor, we show that for every discrete a in the positive part of the unit ball of A it is possible to find a projection p in M such that E(p)=a$. We also show an example of a diffuse operator x in A such that there exists a projection q in M with E(q)=x. These results show a new family of instances of a conjecture by Kadison, the so-called "Carpenter's Theorem".
Cite
@article{arxiv.0802.0031,
title = {Towards the Carpenter's Theorem},
author = {Martin Argerami and Pedro Massey},
journal= {arXiv preprint arXiv:0802.0031},
year = {2011}
}
Comments
Version from July 07