schur multiplier operator and matrix inequalities

In this note, we obtain a reverse version of the haagerup theorem. in particular, if a ∈ mn has a 2 × 2− principal submatrix as[ 1 α β 1] with β = ¯α, then sa > 1 where the operatorsa : mn −→ mn is defined by sa(b) := a ◦ b where ” ◦ ” stands for schur product.