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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.
Hadamards determinant inequality was refined and generalized by Zhang and Yang in [Acta Math. Appl. Sinica 20 (1997) 269-274]. Some special cases of the result were rediscovered recently by Rozanski, Witula and Hetmaniok in [Linear Algebra Appl. 532
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
In 2006 Carbery raised a question about an improvement on the naive norm inequality $|f+g|_p^p leq 2^{p-1}(|f|_p^p + |g|_p^p)$ for two functions in $L^p$ of any measure space. When $f=g$ this is an equality, but when the supports of $f$ and $g$ are d
We survey several significant results on the Bohr inequality and presented its generalizations in some new approaches. These are some Bohr type inequalities of Hilbert space operators related to the matrix order and the Jensen inequality. An eigenval
In this work we provide the best constants of the multiple Khintchine inequality. This allows us, among other results, to obtain the best constants of the mixed $left( ell_{frac{p}{p-1}},ell_{2}right) $-Littlewood inequality, thus ending completely a work started by Pellegrino in cite{pell}.