The Cauchy-Schwarz (C-S) inequality is one of the most famous inequalities in mathematics. In this survey article, we first give a brief history of the inequality. Afterward, we present the C-S inequality for inner product ...

We investigate some relations between Kwong functions and operator monotone functions. As an application, we present an arithmetic–geometric mean type inequality by showing that for two continuous functions f, g on (0,∞)(0,∞) such that View...

Let $A$ and $B$ be two accretive operators. We first introduce the weighted geometric mean of $A$ and $B$ together with some related properties. Afterwards, we define the relative entropy as well as the Tsallis entropy of $A$ and $B$. The present...

‎Let $C$ and $D$ be positive operators such that $C\\leq D$ and $D$ be invertible‎. ‎We show that there exists a trace preserving unital completely positive map $\\Phi_{C,D}:\\mathbb{B}(\\mathcal{H})\\rightarrow ...

In this paper‎, ‎the two-parameter Pareto distribution is considered and the problem of prediction of order statistics from a future sample and that of its geometric mean are discussed‎. ‎The Bayesian approach is applied to construct predictors...

geometric mean and Hadamard products of Hilbert space operators....

We square operator Pólya–Szegö and Diaz–Metcalf type inequalities as follows: If operator inequalities View the MathML source0<m12≤A≤M12 and View the MathML source0<m22≤B≤M22 hold for some positive real numbers ...

‎Let $A,B,$ and $C$ be positive operators in $\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\mathbb{B}(\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\mathscr{H})$‎. ‎The characterization of the operator geometric means by $2\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\times 2$ positive...
}\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\left\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\{U^*TU \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ | \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ U\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\in \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\mathcal{U}(\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\mathscr{H})\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\right\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\}.$$‎
‎We s...

We establish several operator versions of the classical Aczel inequality. One of operator versions deals with the weighted operator geometric mean and another is related to the positive sesquilinear forms. Some applications including the unital...