SUT J. Math. 53 (1), 39-58, (June 2017) DOI: 10.55937/sut/1505482247
KEYWORDS: operator perspective, Convex functions, Operator inequalities, arithmetic mean-geometric mean operator inequality, relative operator entropy, 47A63, 47A30, 15A60, 26D15, 26D10
In this paper we introduce the concept of quadratic operator perspective for a continuous function defined on the positive semi-axis of real numbers, the invertible operator and operator on a Hilbert space by
This generalize the quadratic weighted operator geometric mean of defined by
for and the quadratic relative operator entropy defined by
Some inequalities for this perspective of convex functions are established. Applications for quadratic weighted operator geometric mean and quadratic relative operator entropy are also provided.