Comparison of Various Means for Operators

摘要

For Hilbert space operators H, K, X with H, K>=0 the norm inequality |||H~(1/2)XK~(1/2)|||<=1/2|||HX+XK||| is known, where ||| centre dot ||| 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.