Abstract
Equivalence relations among the Reid inequality, the Löwner-Heinz inequality, and the Heinz-Kato inequality are given. Extensions of these inequalities are given using the Furuta inequality.
Similar content being viewed by others
References
M.Fujii,Furuta's inequality and its mean theoretic approach, J. Operator Theory23(1990), 67–72.
M.Fujii and T.Furuta,Löwner-Heinz, Cordes and Heinz-Kato inequalities, Math. Japon.38(1993), 73–78.
M.Fujii, T.Furuta and R.Nakamoto,Norm inequalities in the Corach-Porta-Recht theory and operator means, in press in Illinois J. Math.
M.Fujii and E.Kamei,Mean theoretic approach to the grand Furuta inequality, Proc. Amer. Math. Soc.124(1996), 2751–2756.
T.Furuta,A≥B≥0 assures (BrApBr)1/q≥B(p+2r)/q for r≥0, p≥0, q≥1 with (1+2r)q≥p+2r, Proc. Amer. Math. Soc.101(1987), 85–88.
T.Furuta,A proof via operator means of an order preserving inequality, Linear Alg. and Its Appl.113(1989), 129–130.
T.Furuta,Elementary proof of an order preserving inequality, Proc. Japan Acad.65(1989), 126.
T.Furuta,Norm inequalities equivalent to Löwner-Heinz theorem Rev in Math Phys.1(1989), 135–137.
T.Furuta,Two operator functions with monotone property, Proc. Amer. Math. Soc.111(1991), 511–516.
T.Furuta,Generalization of Heinz-Kato theorem via Furuta inequality, Operator Theory: Advances and Applications62(1993), 77–83.
T.Furuta,An extension of the Heinz-Kato theorem, Proc. Amer. Math. Soc.120 (1994), 785–787.
T.Furuta,Determinant type generalizations of Heinz-Kato theorem via Furuta inequality, Proc. Amer. Math. Soc.120 (1994), 223–231.
T.Furuta,Extension of the Furuta inequality and Ando-Hiai log-majorization, Linear Alg. and Its Appl.219 (1995), 139–155.
P.R.Halmos,A Hilbert Space Problem Book, Van Nostrand, Princeton, New Jersey 1967.
E. Heinz, Beiträge zur Störungstheorie der Spektralzerlegung, Math. Ann.123(1951), 415–438.
E.Kamei,A satellite to Furuta's inequality, Math. Japon33(1988), 883–886.
T.Kato,Notes on some inequalities for linear operators, Math. Ann.125 (1952), 208–212.
K.Löwner,Über monotone Matrixfunktionen, Math. Z.38(1934), 177–216.
G.K.Pedersen,Some operator monotone functions Proc. Amer. Math. Soc.36(1972), 309–310.
W.T.Reid,Symmetrizable completely continuous linear transformations in Hilbert space, Duke Math. J.18(1951), 41–56.
K,Tanahashi,Best possibility of the Furuta inequality, Proc. Amer. Math. Soc.124 (1996), 141–146.
D.Wang,Löwner-Heinz and Reid inequalities, preprint.
T.Yoshino,Note on Heinz's inequality, Proc. Japan Acad.64(1988), 325–326.
Author information
Authors and Affiliations
Additional information
Dedicated to Professor Zirô Takeda on his 75th birthday with respect and affection
Research supported in part by Grand-in-Aid for Scientific Research.
Rights and permissions
About this article
Cite this article
Furuta, T. Equivalence relations among reid, Löwner-Heinz and Heinz-Kato inequalities, and extensions of these inequalities. Integr equ oper theory 29, 1–9 (1997). https://doi.org/10.1007/BF01191475
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01191475