Towards the carpenter's theorem

Authors:
Martín Argerami and Pedro Massey

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

Published electronically:
June 22, 2009

MathSciNet review:
2529874

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a II factor with trace , a masa and the unique conditional expectation onto . Under some technical assumptions on the inclusion , which hold true for any semiregular masa of a separable factor, we show that for elements in certain dense families of the positive part of the unit ball of , it is possible to find a projection such that . This shows a new family of instances of a conjecture by Kadison, the so-called ``carpenter's theorem''.

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Additional 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

DOI:
https://doi.org/10.1090/S0002-9939-09-09999-7

Keywords:
Diagonals of operators,
Schur-Horn theorem,
conditional expectations

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

Article copyright:
© Copyright 2009
American Mathematical Society