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An operator inequality

✍ Scribed by Frank Hansen

Book ID
105168212
Publisher
Springer
Year
1980
Tongue
English
Weight
79 KB
Volume
246
Category
Article
ISSN
0025-5831

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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