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Dinh Trung Hoa, Hiroyuki Osaka; Jun Tomiyama; Characterization of operator monotone functions by Powers-Stormer type inequalities; Linear and Multilinear Algebra, Vol. 63 (2015), pp. 1577 – 1589 (SCIE).

Abstract

Let be a normal state on the algebra of all bounded operators on a Hilbert space , a strictly positive continuous function on and . We will give characterizations of matrix and operator monotonicity by the following generalized Powers–Størmer type inequality

whenever are positive invertible operators in
 
Keywords
  • operator monotonicity,
  • trace,
  • generalized Powers–Størmer type inequality,
  • normal states,
  • 46L30,
  • 15A45