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Characterization of operator monotone functions by Powers–Størmer type inequalities

Authors: 

Dinh Trung Hoa, Hiroyuki Osaka and Jun Tomiyama

Source title: 
Linear and Multilinear Algebra, 63(8): 1577-1589, 2015 (ISI)
Academic year of acceptance: 
2014-2015
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