島根大学総合理工学部紀要.シリーズB

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島根大学総合理工学部紀要.シリーズB 54
2021-01-30 発行

REVERSE JENSEN INTEGRAL INEQUALITIES FOR CONVEX FUNCTIONS AND POSITIVE LINEAR MAPS IN C∗-ALGEBRAS

DRAGOMIR, S. S.
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内容記述(抄録等)
Let A and B be unital C∗ -algebras. In this paper we obtain several operator inequalities providing upper bounds for the difference
∫Tϕt (f (xt)) dμ (t) -f(∫Tϕt (xt) dμ (t)),
where f : I ! R is a convex function defined on an interval I , (ϕt)t∈T is a unital field of positive linear mappings ϕt : A ! B defined on a locally compact Hausdorff space T with a bounded Radon measure μ and (xt)t∈T is a bounded continuous field of selfadjoint elements in A with spectra contained in I. Several Hermite-Hadamard type inequalities are given. Some examples for convex and operator convex functions are also provided.
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