## Towards the carpenter’s theorem

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- by Martín Argerami and Pedro Massey
- Proc. Amer. Math. Soc.
**137**(2009), 3679-3687 - DOI: https://doi.org/10.1090/S0002-9939-09-09999-7
- Published electronically: June 22, 2009
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## Abstract:

Let $\mathcal {M}$ be a II$_1$ factor with trace $\tau$, $\mathcal {A}\subseteq \mathcal {M}$ a masa and $E_{\mathcal {A}}$ the unique conditional expectation onto $\mathcal {A}$. Under some technical assumptions on the inclusion $\mathcal {A}\subseteq \mathcal {M}$, which hold true for any semiregular masa of a separable factor, we show that for elements $a$ in certain dense families of the positive part of the unit ball of $\mathcal {A}$, it is possible to find a projection $p\in \mathcal {M}$ such that $E_{\mathcal {A}}(p)=a$. This shows a new family of instances of a conjecture by Kadison, the so-called “carpenter’s theorem”.## References

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## Bibliographic Information

**Martín Argerami**- Affiliation: Department of Mathematics, University of Regina, Regina Saskatchewan, Canada
- Email: argerami@math.uregina.ca
**Pedro Massey**- Affiliation: Departamento de Matemática, Universidad Nacional de La Plata and Instituto Argentino de Matemática-conicet, Argentina
- Email: massey@mate.unlp.edu.ar
- Received by editor(s): July 17, 2007
- Published electronically: June 22, 2009
- Additional Notes: The first author was supported in part by the Natural Sciences and Engineering Research Council of Canada

The second author was supported in part by CONICET of Argentina, UNLP, and a PIMS Postdoctoral Fellowship - Communicated by: Marius Junge
- © Copyright 2009 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**137**(2009), 3679-3687 - MSC (2000): Primary 46L99; Secondary 46L55
- DOI: https://doi.org/10.1090/S0002-9939-09-09999-7
- MathSciNet review: 2529874