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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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”.
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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
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