On the minimal members of convex expectations

In this paper, we show that for a convex expectation E[⋅] defined on L1(Ω,F,P), the following statements are equivalent:(i)E is a minimal member of the set of all convex expectations defined on L1(Ω,F,P);(ii)E is linear;(iii)two-dimensional Jensen inequality for E holds. In addition, we prove a sandwich theorem for convex expectation and concave expectation.