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In a recent work, Moslehian and Rajic have shown that the Gruss inequality holds for unital n-positive linear maps $phi:mathcal A rightarrow B(H)$, 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.
D. Bures had defined a metric on the set of normal states on a von Neumann algebra using GNS representations of states. This notion has been extended to completely positive maps between $C^*$-algebras by D. Kretschmann, D. Schlingemann and R. F. Wern
A matrix convex set is a set of the form $mathcal{S} = cup_{ngeq 1}mathcal{S}_n$ (where each $mathcal{S}_n$ is a set of $d$-tuples of $n times n$ matrices) that is invariant under UCP maps from $M_n$ to $M_k$ and under formation of direct sums. We st
We study the symmetrized noncommutative arithmetic geometric mean inequality introduced(AGM) by Recht and R{e} $$ |frac{(n-d)!}{n!}sumlimits_{{ j_1,...,j_d mbox{ different}} }A_{j_{1}}^*A_{j_{2}}^*...A_{j_{d}}^*A_{j_{d}}...A_{j_{2}}A_{j_{1}} | leq
In this article, we explore the celebrated Gr{u}ss inequality, where we present a new approach using the Gr{u}ss inequality to obtain new refinements of operator means inequalities. We also present several operator Gr{u}ss-type inequalities with applications to the numerical radius and entropies.
In this article, we give an abstract characterization of the ``identity of an operator space $V$ by looking at a quantity $n_{cb}(V,u)$ which is defined in analogue to a well-known quantity in Banach space theory. More precisely, we show that there e