Operator convex functions of several variables

Publications of the Research Institute for Mathematical Sciences

Volumn 33, Issue 3, 1997, Pages 443-463

  Hansen, Frank ^a  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0346158227     PISSN: 00345318     EISSN: 16634926     Source Type: Journal    
DOI: 10.2977/prims/1195145324     Document Type: Article

References (16)

1. Ando, T., Concavity of certain maps of positive definite matrices and applications to Hadamard products, Linear Algebra Appl., 26 (1979), 203-241.
2. Araki, H., Expansional in Banach algebras, Ann. Sci. Éc. Norm. Sup., 6 (1973), 67-84.
3. Aujla, J. S., Matrix convexity of functions of two variables, Linear Algebra Appl., 194 (1993), 149-160.
4. Bendat, J. and Sherman, S., Monotone and convex operator functions, Trans. Am. Math. Soc., 79 (1955), 58-71.
5. Brown, A. L. and Vasudeva, H. L., The calculus of operator functions, operator monotonocity and operator convexity, Submitted to Linear Algebra Appl., 1996.
6. Donoghue, W., Monotone matrix functions and analytic continuation. Springer, Berlin, Heidelberg, New York, 1974.
7. Wigner, E. P. and Neumann, J. v., Significance of Loewner's theorem in the quantum theory of collisions, Ann. of Math., 59 (1954), 418-433.
8. Flett, T. M., Differential Analysis, Cambridge University Press, Cambridge, 1980.
9. Hansen, F., An operator inequality, Math. Ann., 246 (1980), 249-250.
10. _, Jensen's operator inequality for functions of two variables, Proc. Amer. Math. Soc, 1996.
11. Hansen, F. and Pedersen, G. K., Jensen's inequality for operators and Löwner's theorem, Proc. Amer. Math. Soc., 125 (1997), 2093-2102.
12. _, Perturbation formulas for traces on C*-algebras, Publ. RIMS, Kyoto Univ., 31 (1995), 169-178.
13. Kadison, R. V. and Ringrose, J. R., Fundamentals of the Theory of Operator Algebras, I-II., Academic Press, 1982 & 1986.
14. Korányi, A., On some classes of analytic functions of several variables, Trans Amer. Math. Soc., 101 (1961), 520-554.
15. Kraus, F., Über konvekse Matrixfunktionen, Math. Z., 41 (1936), 18-42.
16. Löwner, K., Über monotone Matrixfunktionen, Math. Z., 38 (1934), 177-216.