Acta mathematica scientia, Series B >
AN ORDER PRESERVING INEQUALITY FOR THREE OPERATORS VIA FURUTA INEQUALITY
Received date: 2005-12-30
Revised date: 2006-11-27
Online published: 2008-10-20
Furuta showed that if A ≥ B ≥0, then for each r≥0, f(p)=(Ar/2BpAr/2)t+r/p+r
is decreasing for p≥t≥0. Using this result, the following inequality (Cr/2AB2A)δCr/2)p-1+r/4δ+r≤Cp-1+r is obtained for 0<p≤1, r≥1, 1/4≤δ≤1 and three positive operators A, B, C satisfy (A1/2 B A1/2)p/2 ≤ Ap, (B1/2 AB1/2)p/2 ≥ Bp, (C1/2 AC1/2)p/2 ≤Cp, (A1/2 CA1/2)p/2≥Ap.
Key words： Positive operator; Furuta inequality; operator inequality
Yang Changsen . AN ORDER PRESERVING INEQUALITY FOR THREE OPERATORS VIA FURUTA INEQUALITY[J]. Acta mathematica scientia, Series B, 2008 , 28(4) : 998 -002 . DOI: 10.1016/S0252-9602(08)60099-5
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