Abstract
Let f be a continuous convex function on an interval J, let A, B, C, D be self-adjoint operators acting on a Hilbert space with spectra contained in J such that A+D=B+C and A⩽m⩽B,C⩽M⩽D for two real numbers m<M, and let Φ be a unital positive linear map on B(H). We prove the inequalityf(Φ(B))+f(Φ(C))⩽Φ(f(A))+Φ(f(D))and apply it to obtain several inequalities such as the Jensen–Mercer operator inequality and the Petrović operator inequality.
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