On the Gruss Inequality for unital 2-positive linear maps

2015/09/30 by Sriram Balasubramanian, Balasubramanian, Sriram
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.FA #math.OA

paper · pdf · doi:10.48550/arxiv.1509.09040

7 Pages

arxiv created 2016/04/04 · arxiv updated 2016/04/05

Abstract

In a recent work, Moslehian and Rajic have shown that the Gruss inequality holds for unital n-positive linear maps ϕ:\mathcal A → B(H), where \mathcal 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.

Related

• Some generalisations of the inequalities for positive linear maps
• A remark on some inequalities for positive linear maps
• A Gruss type inequality for vector-valued functions in Hilbert C*-modules
• Gruss type inequalities in semi-inner product C*-modules and applications
• Linear maps preserving regularity in C∗-algebras