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 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''.
- 1. M. Argerami and P. Massey, A Schur-Horn theorem in 𝐼𝐼₁ factors, Indiana Univ. Math. J. 56 (2007), no. 5, 2051–2059. MR 2359722, https://doi.org/10.1512/iumj.2007.56.3113
- 2. William Arveson, Diagonals of normal operators with finite spectrum, Proc. Natl. Acad. Sci. USA 104 (2007), no. 4, 1152–1158. MR 2303566, https://doi.org/10.1073/pnas.0605367104
- 3. William Arveson and Richard V. Kadison, Diagonals of self-adjoint operators, Operator theory, operator algebras, and applications, Contemp. Math., vol. 414, Amer. Math. Soc., Providence, RI, 2006, pp. 247–263. MR 2277215, https://doi.org/10.1090/conm/414/07814
- 4. Richard V. Kadison, The Pythagorean theorem. I. The finite case, Proc. Natl. Acad. Sci. USA 99 (2002), no. 7, 4178–4184. MR 1895747, https://doi.org/10.1073/pnas.032677199
- 5. Richard V. Kadison, The Pythagorean theorem. I. The finite case, Proc. Natl. Acad. Sci. USA 99 (2002), no. 7, 4178–4184. MR 1895747, https://doi.org/10.1073/pnas.032677199
- 6. Sorin Popa, On a problem of R. V. Kadison on maximal abelian ∗-subalgebras in factors, Invent. Math. 65 (1981/82), no. 2, 269–281. MR 641131, https://doi.org/10.1007/BF01389015
- 7. Sorin Popa, Orthogonal pairs of ∗-subalgebras in finite von Neumann algebras, J. Operator Theory 9 (1983), no. 2, 253–268. MR 703810
- 8. Allan M. Sinclair and Roger R. Smith, Finite von Neumann algebras and masas, London Mathematical Society Lecture Note Series, vol. 351, Cambridge University Press, Cambridge, 2008. MR 2433341
Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46L99, 46L55
Retrieve articles in all journals with MSC (2000): 46L99, 46L55
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