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Inequalities and solution of an operator equation

โœ Scribed by Chuanxi Zhu; Zongben Xu


Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
174 KB
Volume
21
Category
Article
ISSN
0893-9659

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Given bounded positive invertible operators A and B on a Hilbert space H, it is shown that the inequality AXA -1 + B -1 XB 2 X holds for all bounded operators X of rank 1 if and only if B = f (A) for some increasing function f satisfying a certain simple inequality, which in the case when the spectr