Gr\\"{u}ss showed that if $f$ and $g$ are integrable real functions on $[a, b]$ and there exist real constants $\\alpha,\\beta,\\gamma,\\Gamma$ such that $\\alpha\\leq f (x)\\leq \\beta$ and

$\\gamma\\leq g(x)\\leq \\Gamma$ for all $x\\in [a...

Assuming a unitarily invariant norm $...
|\\cdot...
|$ is given on a two-sided ideal of bounded linear operators acting on a separable Hilbert space, it induces some unitarily invariant norms $...
|\\cdot...
|$ on matrix algebras $\\mathcal{M}_n$ for all finite values of $n$ via $...
|A...
|=...
|A\\oplus 0...
|$. We show that if $\\mathscr{A}$ is a $C^*$-algebra of finite dimension

$k$ and $\\Phi: \\mathscr{A} \\to \\mathcal{M}_n$ is a unital completely

positive map, then

\\begin{equation*}

...
|\\Phi(AB)-\\Phi(A)\\Phi(B)...
| \\leq \\frac{1}{4}

...
|I_{n}...
|\\,...
|I_{kn}...
{M}_{m}$. Further we get an analogous

inequality for certain $n$-positive maps in the setting of full

matrix algebras by using some matrix tricks. We also give a Gr\\"uss

operator inequality in the setting of $C^*$-algebras of arbitrary...

Let $\\mathcal{A}$ and $\\mathcal{B}$ be two unital $C^*$-algebras and let for $C\\in\\mathcal{A},\\ \\Gamma_C=\\{\\gamma \\in \\mathbb{C} : \\|C-\\gamma I\\|=\\inf_{\\alpha\\in \\mathbb{C}} \\|C-\\alpha I\\|\\}$. We prove ...

Wheeler (1964) had formulated Mach’s principle as the boundary condition for general relativistic field equations. Here, we use this idea and develop a modified dynamical model of cosmology based on imposing Neumann boundary ...