Differential geometry for nuclear positive operators

Integral Equations and Operator Theory

Volumn 57, Issue 4, 2007, Pages 451-471

  Conde, Cristian ^a  

^a NONE   (Argentina)

Author keywords

Finsler metric; Non positive curvature; Nuclear positive operators; Reductive homogeneous space

Indexed keywords

EID: 34047156686     PISSN: 0378620X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00020-006-1465-x     Document Type: Article

References (21)

1. J. Aubin, Optima and Equilibria - An introduction to nonlinear analysis. 2nd Edition, Springer Verlag, 1998.
2. E. Andruchow and L. Recht, Sectional curvature and commutation of pairs of seladjoint operators. Journal of Operator Theory (to appear).
3. T. Ando; R. Horn and Ch. Johnson, The Singular Values of a Hadamard product: a basic inequality. Linear Multinear Algebra 21 (1987), 345-365.
4. W. Ballmann; M. Gromov and V. Schroeder, Manifolds of non positive curvature. Birkhuser Verlag, 1985.
5. R. Bhatia, On the exponential metric increasing property. Linear Algebra and its applications 375 (2003), 211-220.
6. G. Corach; H. Porta and L. Recht, A geometric interpretation of Segals inequality. Proc. Amer. Math. Soc. 115 (1992), 229-231.
7. G. Corach; H. Porta and L. Recht, The geometry of spaces of selfadjoint invertible elements of a C*-algebra. Integral Equations and Operator Theory 16 (1993), 333-359.
8. G. Corach; H. Porta and L. Recht, Convexity of the geodesic distance on spaces of positive operators. Illinois Journal of Mathematics 38 N l (1994), 87-94.
9. Erdelyi, A. et al.: Tables of integral transforms. (The Bateman manuscript), Volumen 1, Mc Graw Hill, 1954.
10. M. Fujii; R. Furuta and R. Nakamoto, Norm inequalities in the Corach-Porta-Recht theory and operator means. Illinois Journal of Mathematics 40 N 4 (1996), 1-8.
11. J. Fujii and E. Kamei, Relative operator entropy in nonconmutative information theory. Mathematica Japonica 34 (1989), 341-348.
12. P. de la Harpe, Classical Banach-Lie Algebras and Banach-Lie Groups of Operators in Hilbert Space. Lecture Notes in Mathematics 285, Springer-Verlag, 1972.
13. F. Hiai and H. Kosaki, Comparison of various Means of operators. Journal of Functional Analysis 163 (1999), 300-323.
14. J. Jost, Nonpositive Curvature: Geometric and Analytic Aspects, Birkhuser Verlag, 1997.
15. S. Lang, Differential and Riemannian Manifolds, Springer, 1995.
16. L. Mata Lorenzo and L. Recht, Infinite Dimensional Homogeneous Reductive Spaces. Acta Cientfica Venezolana 43 No 2 (1992), 76-90.
17. J. Milnor, Morse Theory Annals of Mathematical Studies 54, Princeton University Press, 1963.
18. G. Mostow, Some new decomposition theorems for semi-simple groups, Mem. Amer. Math. Soc. 14 (1955), 31-54.
19. W. Pusz and S. Woronowicz, Functional Calculus for sesquilinear forms and the purification map. Rep. Math. Phys. 8 (1975), 159-170.
20. W. Rudin, Real and Complex Analysis, Tata Mc Graw Hill, 1974.
21. A. Uhlmann, Density operators as an arena for differential geometry. Rep. Math. Phys. 36 (1993), 253-263.