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Comparison of Various Means for Operators

✍ Scribed by Fumio Hiai; Hideki Kosaki

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
173 KB
Volume
163
Category
Article
ISSN
0022-1236

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✦ Synopsis

For Hilbert space operators H, K, X with H, K 0 the norm inequality _H 1Γ‚2 XK 1Γ‚2 _ 1 2 _HX+XK_ is known, where _ } _ is an arbitrary unitarily invariant norm. A refinement of this arithmetic geometric mean inequality is studied. Similar norm inequalities are indeed established for various natural means for operators such as the logarithmic mean.

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