ON THE GRUSS INEQUALITY FOR UNITAL 2-POSITIVE LINEAR MAPS

In a recent work, Moslehian and Rajic have shown that the Gruss inequality holds for unital n-positive linear maps phi : A > B(H), where A is a unital C*-algebra and H is a Hilbert space, if n >= 3. They also demonstrate that the inequality fails to hold, in general, if n = 1 and question whether the inequality holds if n = 2. In this article, we provide an affirmative answer to this question.