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An operator inequality and its consequences

✍ Scribed by Moslehian, M.S.; Mićić, J.; Kian, M.

Book ID
120390077
Publisher
Elsevier Science
Year
2013
Tongue
English
Weight
274 KB
Volume
439
Category
Article
ISSN
0024-3795

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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