Towards the Carpenter's Theorem

Details Towards the Carpenter's Theorem Towards the Carpenter's Theorem

2008-01-31

arxiv.org/abs/0802.0031v1

Proc. Am. Math. Soc., 137 (2009), 3679-3687

Mathematics

Operator Algebras

Version from July 07

Scientific paper

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".

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