‎Let BJ(H) denote the set of self-adjoint operators acting on a Hilbert space H with spectra contained in an open interval J. A map Φ:BJ(H)→B(H)sa is said to be of Jensen-type if (C∗AC+D∗BD)≤C∗Φ(A)C+D∗Φ(B)D for all A,B∈BJ(H) and bounded linear operators C, D acting on H with C∗C+D∗D=I, where I denotes the identity operator. We show that a Jensen-type map on an infinite dimensional Hilbert space is of the form Φ(A)=f(A) for some operator convex function f defined in J.

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