Positive definite functions and operator inequalities

Bulletin of the London Mathematical Society

Volumn 32, Issue 2, 2000, Pages 214-228

  Bhatia, Rajendra ^a   Parthasarathy, K R ^a  

^a INDIAN STATISTICAL INSTITUTE   (India)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040971933     PISSN: 00246093     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0024609399006797     Document Type: Article

References (30)

1. T. ANDO, Topics on operator inequalities (Hokkaido University, Sapporo, 1978).
2. T. ANDO, 'Majorizations and inequalities in matrix theory', Linear Algebra Appl. 199 (1994) 17-67.
3. R. BHATIA, Matrix analysis (Springer, New York, 1997).
4. R. BHATIA and C. DAVIS, 'More matrix forms of the arithmetic-geometric mean inequality', SIAM J. Matrix Anal. Appl. 14 (1993) 132-136.
5. G. CORACH, H. PORTA and L. RECHT, 'An operator inequality', Linear Algebra Appl. 142 (1990) 153-158.
6. G. CORACH, H. PORTA and L. RECHT, 'Jacobi fields on space of positive operators', Linear Algebra Appl. 179 (1993) 271-275.
7. C. DAVIS, 'Notions generalizing convexity for functions defined on spaces of matrices', Convexity, Proc. Sympos. Pure Math. 8 (Amer. Math. Soc., Providence, RI, 1963).
8. W. F. DONOGHUE, Monotone matrix functions and analytic continuation (Springer, New York, 1974).
9. J. FUJII, M. FUJII, T. FURUTA and R. NAKAMOTO, 'Norm inequalities equivalent to Heinz inequality', Proc. Amer. Math. Soc. 118 (1993) 827-830.
10. T. FURUTA, 'Norm inequalities equivalent to Löwner-Heinz theorem', Rev. Math. Phvs. 1 (1989) 135-137.
11. I. S. GRADSHTEYN and I. M. RYZHIK, Tables of integrals, series, and products (5th edn, Academic Press, New York, 1994).
12. F. HANSEN and G. K. PEDERSEN, 'Jensen's inequality for operators and Löwner's theorem', Math. Ann. 258 (1982) 229-241.
13. E. HEINZ, 'Beiträge zur Störungstheorie der Spektralzerlegung', Math. Ann. 123 (1951) 415-438.
14. H. HELSON, Harmonic analysis (2nd edn. Hindustan Book Agency, Delhi, 1995).
15. F. HIAI and H. KOSAKI, 'Comparison of various means for operators', J. Funct. Anal. 163 (1999) 300-323.
16. F. HIAI and H. KOSAKI, 'Means for matrices and comparison of their norms', Preprint 1998-23, Kyushu University, Fukuoka; Indiana Univ. Math. J., to appear.
17. R. A. HORN, 'Norm bounds for Hadamard products and the arithmetic-geometric mean inequality for unitarily invariant norms', Linear Algebra Appl. 223/224 (1995) 355-361.
18. R. A. HORN and C. R. JOHNSON, Matrix analysis (Cambridge University Press, New York, 1985).
19. R. A. HORN and C. R. JOHNSON, Topics in matrix analysis (Cambridge University Press, New York, 1990).
20. H. KOSAKI, 'Arithmetic-geometric mean and related inequalities for operators', J. Funct. Anal. 156 (1998) 429-451.
21. M. K. KWONG, 'On the definiteness of the solutions of certain matrix equations', Linear Algebra Appl. 108 (1988) 177-197.
22. M. K. KWONG, 'Some results on matrix monotone functions', Linear Algebra Appl. 118 (1989) 129-153.
23. C. LOEWNER, 'Advanced matrix theory', Mimeographed Lecture Notes, Stanford University, Winter 1957.
24. K. LÖWNER, 'Über monotone Matrixfunctionen', Math. Z. 38 (1934) 177-216.
25. A. W. MARSHALL and I. OLKIN, Inequalities: theory of majorization and its applications (Academic Press, New York, 1979).
26. R. MATHIAS, 'An arithmetic-geometric mean inequality involving Hadamard products', Linear Algebra Appl. 184 (1993) 71-78.
27. A. MCINTOSH, 'Heinz inequalities and perturbation of spectral families', Report 79-0006, Macquarie University, North Ryde, 1979.
28. F. OBERHETTINGER, Tables of Fourier transforms and Fourier transforms of distributions (Springer, Berlin, 1990).
29. Z. SASVÁRI, Positive definite and definitizable functions (Akademie, Berlin, 1994).
30. X. ZHAN, 'Inequalities for unitarily invariant norms', SIAM J. Matrix Anal. 20 (1999) 466-470.