Reverse inequalities of Araki, Cordes and Löwner–Heinz inequalities. (English) Zbl 1111.47011

Fujii, Masatoshi; Seo, Yuki

Nihonkai Math. J. 16, No. 2, 145-154 (2005).

It was shown in [T. Furuta, Rev. Math. Phys. 1, 135–137 (1989; Zbl 0725.47008)] that the Löwner–Heinz, Araki and Cordes inequalities can be obtained by using each other. In the present paper, the authors give Kantorovich type reverse inequalities of Araki and Cordes. Then they show that reverse inequalities of Löwner–Heinz, Araki and Cordes can be obtained by using each other.

Reviewer: Takeaki Yamazaki (Yokohama)

MSC:

47A30	Norms (inequalities, more than one norm, etc.) of linear operators
47A63	Linear operator inequalities

Keywords:

Kantorovich inequality; Kantorovich constant; operator inequality; Cordes inequality; Löwner-Heinz inequality; Araki’s inequality

Citations:

Zbl 0725.47008