On the Gruss Inequality for unital 2-positive linear maps

Abstract

In a recent work, Moslehian and Rajic have shown that the Gruss inequality holds for unital n-positive linear maps $\varphi :\mathcal{A}\to B(H)$, where $\mathcal{A}$ is a unital C*-algebra and H is a Hilbert space, if $n\ge 3$. 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.

arXiv comment7 Pages