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Eigenvalue inequalities in an embeddable factor

Author(s): Hari Bercovici; Wing Suet Li
Journal: Proc. Amer. Math. Soc. 134 (2006), 75-80.
MSC (2000): Primary 15A42; Secondary 46L10
Posted: June 14, 2005
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Abstract: We provide a characterization of the possible eigenvalues of the sum of two selfadjoint elements of a II$_{1}$ factor which can be embedded in the ultrapower $\mathcal{R}^{\omega }$ of the hyperfinite II$_{1}$ factor.

References:

1.
H. Bercovici, W.-S. Li, Inequalities for eigenvalues of sums in a von Neumann algebra, Operator Theory: Advances and Applications 127 (2001), 113-126. MR 1902797 (2003d:46082)

2.
H. Bercovici, W.S. Li, and T. Smotzer, Continuous versions of the Littlewood-Richardson rule, selfadjoint operators, and invariant subspaces, J. Operator Theory, to appear.

3.
A. Connes, Classification of injective factors. Cases II$_{1}$, II $_{\infty },$ III $_{\lambda }$, $\lambda \not =1$, Ann. of Math. (2) 104 (1976), no. 1, 73-115. MR 0454659 (56:12908)

4.
T. Fack, Sur la notion de valeur caractéristique, J. Operator Theory 7 (1982), 307-333. MR 0658616 (84m:47012)

5.
T. Fack and H. Kosaki, Generalized $s$-numbers of $\tau $-measurable operators, Pacific J. Math. 123 (1986), no. 2, 269-300. MR 0840845 (87h:46122)

6.
W. Fulton, Eigenvalues, invariant factors, highest weights, and Schubert calculus, Bull. Amer. Math. Soc. (N.S.) 37 (2000), 209-249.MR 1754641 (2001g:15023)

7.
A. Grothendieck, Réarrangements de fonctions et inégalités de convexité dans les algébres de von Neumann munies d'une trace , Séminaire Bourbaki 3 Exp. No. 113 (1959), 127-139. MR 1611379

8.
A. Horn, Eigenvalues of sums of Hermitian matrices, Pacific J. Math. 12 (1962), 225-241. MR 0140521 (25:3941)

9.
A. Klyachko, Stable bundles, representation theory and Hermitian operators, Selecta Math. (N.S.) 4 (1998) no. 3, 419-445. MR 1654578 (2000b:14054)

10.
R. Thompson and L. Freede, On the eigenvalues of sums of Hermitian matrices, Linear Algebra and Appl. 4 (1971), 369-376. MR 0288132 (44:5330)

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Additional Information:

Hari Bercovici
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405

Wing Suet Li
Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332

DOI: 10.1090/S0002-9939-05-07952-9
PII: S 0002-9939(05)07952-9
Received by editor(s): January 8, 2004
Received by editor(s) in revised form: September 2, 2004
Posted: June 14, 2005
Additional Notes: The authors were supported in part by grants from the National Science Foundation. The second author expresses her gratitude to the Department of Mathematics of Indiana University for its kind hospitality while this paper was written.
Communicated by: Joseph A. Ball
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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