Non-commutative Schur-Horn theorems and extended majorization for Hermitian matrices

Linear and Multilinear Algebra

Volumn 58, Issue 4, 2010, Pages 465-480

  Massey, Pedro G ^a  

^a UNIVERSIDAD NACIONAL DE LA PLATA   (Argentina)

Author keywords

Diagonal block compressions; Extended majorization; Non commutative Schur Horn theorems; Partial traces; Unitary orbit

Indexed keywords

EID: 77951934022     PISSN: 03081087     EISSN: 15635139     Source Type: Journal    
DOI: 10.1080/03081080802677615     Document Type: Article

References (27)

1. T. Ando, Majorization, doubly stochastic matrices and comparison of eigenvalues, Hokkaido University, Research Institute of Applied Electricity, Division of Applied Mathematics, Sapporo, 1982, pp. ii+87.
2. J. Antezana, P. Massey, M. Ruiz, and D. Stojanoff, The Schur-Horn theorem for operators and frames with prescribed norms and frame operator, Illinois J. Math. 51 (2007), pp. 537-560.
3. J. Antezana, P. Massey, and D. Stojanoff, Jensen's inequality and majorization, J. Math. Anal. Appl. 331 (2007), pp. 297-307.
4. M. Argerami and P. Massey, A Schur-Horn theorem for II1 factors, Indiana Univ. Math. J. 56 (2007), pp. 2051-2059.
5. W. Arveson and R.V. Kadison, Diagonals of self-adjoint operators, in Operator Theory, Operator Algebras, and Applications, Contemp. Math., Vol. 414, American Mathematical Society, Providence, RI, 2006, pp. 247-263.
6. M. Atiyah, Convexity and commuting Hamiltonians, Bull. L.M.S. 14 (1982), pp. 1-15.
7. J.S. Aujla and J.C. Bourin, Eigenvalue inequalities for convex and log-convex functions, Lin. Alg. Appl. 424 (2007), pp. 25-35.
8. J.S. Aujla and F.C. Silva, Weak majorization inequalities and convex functions, Lin. Alg. Appl. 369 (2003), pp. 217-233.
9. R. Bhatia, Partial traces and entropy inequalities, Lin. Alg. Appl. 370 (2003), pp. 125-132.
10. I.S. Dhillon, R.W. Heath Jr, M.A. Sustik, and J.A. Tropp, Generalized finite algorithms for constructing Hermitian matrices with prescribed diagonal and spectrum, SIAM J. Matrix Anal. Appl. 27 (2005), pp. 61-71.
11. S. Friedland, Finite and infinite-dimensional generalizations of Klyachko's theorem, Lin. Alg. Appl. 319 (2000), pp. 3-22.
12. W. Fulton, Eigenvalues of majorized Hermitian matrices and Littlewood-Richardson coefficients, Lin. Alg. Appl. 319 (2000), pp. 23-36.
13. W. Fulton, Eigenvalues, invariant factors, highest weights, and Schubert calculus, Bull. Amer. Math. Soc. 37 (2000), pp. 209-249 (math.AG/9908012).
14. V. Guillemin and S. Sternberg, Convexity properties of the moment mapping, Invent. Math. 67 (1982), pp. 491-513.
15. A. Horn, Doubly stochastic matrices and the diagonal of a rotation matrix, Amer. J. Math. 76 (1954), pp. 620-630.
16. R. Kadison, The Pythagorean theorem: I. The finite case, PNAS 99 (2002), pp. 4178-4184.
17. R. Kadison, The Pythagorean theorem: II. The infinite discrete case, PNAS 99 (2003), pp. 5217-5222.
18. A.A. Klyachko, Stable bundles, representation theory and Hermitian operators, Selecta Math. 4 (1998), pp. 419-445.
19. B. Konstant, On convexity, the Weyl group and the Iwasawa decomposition, Ann. Scient. Éc. Norm. Sup. 6 (1973), pp. 413-455.
20. R.S. Leite, T.R.W. Richa, and C. Tomei, Geometric proofs of some theorems of Schur-Horn type, Lin. Alg. Appl. 286 (1999), pp. 149-173.
21. C.K. Li and Y.T. Poon, Principal submatrices of a Hermitian matrix, Lin. Multilin. Alg. 51 (2003), pp. 199-208.
22. F.M. Peria, P. Massey, and L. Silvestre, Weak matrix majorization, Lin. Alg. Appl. 403 (2005), pp. 343-368.
23. P. Massey, Optimal reconstruction systems for erasures and for the q-potential (submitted).
24. P. Massey and M. Ruiz, Some convex functionals over frame operators, Adv. Comp. Math. (in press).
25. A. Neumann, An infinite-dimensional version of the Schur-Horn convexity theorem, J. Funct. Anal. 161 (1999), pp. 418-451.
26. M.B. Ruskai, Some open problems in QIT (preprint).
27. I. Schur, Über eine klasse von mittlebildungen mit anwendungen auf der determinantentheorie, Sitzungsber. Berliner Mat. Ges. 22 (1923), pp. 9-29.