A characterization of chaotic order

作者：Yang Changsen^*; Gao Fugen

来源：Journal of Inequalities and Applications, 2006, 79123.

DOI：10.1155/JIA/2006/79123

The chaotic order A >> B among positive invertible operators A, B > 0 on a Hilbert space is introduced by logA >= logB. Using Uchiyama's method and Furuta's Kantorovich-type inequality, we will point out that A >> B if and only if parallel to B(p)A(-p/2)B(-p/2)parallel to A(p) >= B-p holds for any 0 < p < p(0), where p(0) is any fixed positive number. On the other hand, for any fixed p(0) > 0, we also show that there exist positive invertible operators A, B such that parallel to B(p)A(-p/2)B(-p/2) parallel to A(p) >= B-p holds for any p >= p(0), but A >> B is not valid.

• 出版日期2006
• 单位河南师范大学