The local form of doubly stochastic maps and joint majorization in II 1 factors

Integral Equations and Operator Theory

Volumn 61, Issue 1, 2008, Pages 1-19

  Argerami, Martín ^a   Massey, Pedro ^b  

^a UNIVERSITY OF REGINA   (Canada)

^b UNIVERSIDAD NACIONAL DE LA PLATA   (Argentina)

Author keywords

Convex hull; Doubly stochastic map; Joint majorization; Unitary orbit.

Indexed keywords

EID: 44649143236     PISSN: 0378620X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00020-008-1569-6     Document Type: Article

References (27)

1. P.M. Alberti and A. Uhlmann, Stochasticity and partial order. Doubly stochastic maps and unitary mixing. Mathematische Monographien, 18. VEB Deutscher Verlag der Wissenschaften, Berlin, 1981.
2. P.M. Alberti, and A. Uhlmann, Dissipative motion in state spaces. Teubner-Texte zur Mathematik, 33. BSB B. G. Teubner Verlagsgesellschaft, Leipzig, 1981.
3. E.M. Alfsen, Compact Convex Sets and Boundary Integrals, Springer-Verlag, New York, NY 1971.
4. T. Ando, Majorization, doubly stochastic matrices and comparison of eigenvalues, Lecture Notes, Hokkaido Univ., 1982.
5. J. Antezana, P. Massey, and D. Stojanoff, Jensen's Inequality and Majorization, J. Math. Anal. App. 331 1 (2007), 297-307.
6. 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. of Math. 51 2 (2007), 537-560.
7. 1 factors, Indiana Univ. Math. J., 56, 5 (2007), 2051-2060.
8. 1 factors, J. Math. Anal. App., 337, 1 (2008), 231-238.
9. W. Arveson, Subalgebras of C*-algebras Acta, Math. 123 (1969), 141-224.
10. W. Arveson and R. Kadison, Diagonals of self-adjoint operators, In D. R. Larson D. Han, P. E. T. Jorgensen, editor, Operator theory, operator algebras and applications, Contemp. Math. Amer. Math. Soc., 2006.
11. G. Birkhoff, Three observations on linear algebra. (Spanish) Univ. Nac. Tucumán. Revista A. 5 (1946), 147-151.
12. J.B. Conway, A course in functional analysis, Springer-Verlag, New York, NY 1990.
13. T. Fack, Sur la notion de valeur caractéristique, J. Operator Theory (1982), 307-333.
14. D.R. Farenick and S.M. Manjegani, Young's Inequality in Operator Algebras, J. Ramanujan Math. Soc. 20, 2 (2005), 107-124.
15. F. Hiai, Majorization and Stochastic maps in von Neumann algebras, J. Math. Anal. Appl. 127, 1 (1987), 18-48.
16. F. Hiai, Spectral majorization between normal operators in von Neumann algebras, Operator algebras and operator theory (Craiova, 1989), 78-115, Pitman Res. Notes Math. Ser., 271, Longman Sci. Tech., Harlow, 1992.
17. F. Hiai and Y. Nakamura, Closed Convex Hulls of Unitary Orbits in von Neumann Algebras, Trans. Amer. Math. Soc. 323 (1991), 1-38.
18. R. Kadison, The Pythagorean theorem I: the finite case, Proc. N.A.S. (USA), 99, 7 (2002), 4178-4184.
19. R. Kadison, The Pythagorean theorem II: the infinite discrete case, Proc. N.A.S. (USA), 99, 8 (2002), 5217-5222.
20. R. Kadison and J. Ringrose, Fundamentals of the Theory of Operator Algebras, Vol. II, Academic Press, Orlando, Florida, 1986.
21. E. Kamei, Majorization in finite factors, Math. Japonica 28, 4 (1983), 495-499.
22. F.D. Martínez Pería, P. Massey, L. Silvestre, Weak matrix majorization. Linear Algebra Appl. 403 (2005), 343-368.
23. 1 factors, J. Operator Theory, to appear.
24. A. Neumann, An infinite-dimensional version of the Schur-Horn convexity theorem, J. Funct. Anal. 161 (1999), 418-451.
25. W. Rudin, Real and complex analysis. Third edition. McGraw-Hill Book Co., New York, 1987.
26. D. Sherman, Unitary orbits of normal operators in von Neumann algebras, Journal fur die Reine und Angewandte Mathematik 605 (2007), 95-132.
27. M. Takesaki, Theory of Operator Algebras I, Encyclopaedia of Mathematical Sciences V, Springer Verlag, 2nd printing of the First Edition 1979.