Mean theoretic approach to the grand Furuta inequality

Proceedings of the American Mathematical Society

Volumn 124, Issue 9, 1996, Pages 2751-2756

  Fujii, Masatoshi ^a   Kamei, Eizaburo ^b  

^a OSAKA KYOIKU UNIVERSITY   (Japan)

^b Momodani Senior Highschool   (Japan)

Author keywords

Ando Hiai inequality; Furuta inequality; Grand Furuta inequality; L wner Heinz inequality; Positive operators

Indexed keywords

EID: 21444459455     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9939-96-03342-4     Document Type: Article

References (17)

1. T.Ando, On some operator inequalities, Math. Ann., 279 (1987), 157-159. MR 89c:47019
2. T.Ando and F.Hiai, Log-majorization and complementary Golden-Thompson type inequalities, Linear Alg. and its Appl., 197/198 (1994), 113-131. MR 95d:15006
3. M.Fujii, Furuta's inequality and its mean theoretic approach, J. Operator theory, 23 (1990), 67-72. MR 91g:47012
4. M.Fujii, T.Furuta and E.Kamei, Furuta's inequality and its application to Ando's Theorem, Linear Alg. and its Appl., 149 (1991), 91-96. MR 92e:47023
5. M.Fujii, T.Furuta and E.Kamei, Operator functions associated with Furuta's inequality, Linear Alg. and its Appl., 179 (1993), 161-169. MR 93j:47026
6. M.Fujii and E.Kamei, Furuta's inequality and a generalization of Ando's Theorem, Proc. Amer. Math. Soc., 115 (1992), 409-413. MR 92i:47108
7. (P+2r)/q for r ≥ 0,p ≥ 0,q ≥ 1 with (1 + 2r)q ≥ p + 2r, Proc. Amer. Math. Soc., 101 (1987), 85-88. MR 89b:47028
8. T.Furuta, Elementary proof of an order preserving inequality, Proc. Japan Acad., 65 (1989), 126. MR 90g:47029
9. T.Furuta, A proof via operator means of an order preserving inequality, Linear Alg. and its Appl., 113 (1989), 12-130. MR 89k:47023
10. T.Furuta, Two operator functions with monotone property, Proc. Amer. Math. Soc., 111 (1991), 511-516. MR 91f:47023
11. T.Furuta, Application of an order preserving inequalities, Operator theory : Advances and Applications, Birkhouser Verlag, Basel, 59 (1992), 180-190. MR 94m:47033
12. T.Furuta, Extension of the Furuta inequality and Ando-Hiai log-majorization, Linear Alg. and its Appl., 219 (1995), 139-155.
13. E.Heinz, Beiträge zur Störungstheorie der Spektralzerlegung, Math. Ann., 123 (1951), 415-438. MR 13:471f
14. E.Kamei, Furuta's inequality via operator means, Math. Japon., 33 (1988), 737-739. MR 90c:47037
15. E.Kamei, A satellite to Furuta's inequality, Math. Japon., 33 (1988), 883-886. MR 89m:47011
16. F.Kubo and T.Ando, Means of positive linear operators, Math. Ann., 246 (1980), 205-224. MR 84d:47028
17. K.Löwner, Über monotone Matrixfunktionen, Math. Z., 38 (1934), 177-216.