Related papers: Operator mean inequalities for sector matrices

We prove some refinements of a reverse AM-GM operator inequality due to M. Lin [Studia Math. 2013;215:187-194]. In particular, we show the operator inequality \begin{eqnarray*} \Phi^p\left(A\nabla_\nu B+2rMm(A^{-1}\nabla B^{-1}-A^{-1}\sharp…

In this article, we employ a standard convex argument to obtain new and refined inequalities related to the matrix mean of two accretive matrices, the numerical radius and the Tsallis relative operator entropy.

For positive definite matrices $A$ and $B$, the Kubo-Ando matrix power mean is defined as $$ P_\mu(p, A, B) = A^{1/2}\left(\frac{1+(A^{-1/2}BA^{-1/2})^p}{2}\right )^{1/p} A^{1/2}\quad (p \ge 0). $$ In this paper, for $0\le p \le 1 \le q$,…

This note aims to present some reverse inequalities about the power means and Karcher mean via the Kantorovich constant and some of these have been generalized to higher power. Also, we generalize the reverse weighted arithmetic-geometric…

We give an upper bound for the weighted geometric mean using the weighted arithmetic mean and the weighted harmonic mean. We also give a lower bound for the weighted geometric mean. These inequalities are proven for two invertible positive…

In this paper, we present some operator and eigenvalue inequalities involving operator monotone, doubly concave and doubly convex functions. These inequalities provide some variants of operator Acz\'{e}l inequality and its reverse via…

Let $\sigma$ be a non-trivial operator mean in the sense of Kubo and Ando, and let $OM_+^1$ the set of normalized positive operator monotone functions on $(0, \infty)$. In this paper, we study class of $\sigma$-subpreserving functions $f\in…

This paper presents a number of Kantorovich type integral inequalities involving tensor products of continuous fields of bounded linear operators on a Hilbert space. Kantorovich type inequality in which the product is replaced by an…

Let $A$ and $ B$ be $n\times n$ positive definite complex matrices, let $\sigma$ be a matrix mean, and let $f : [0,\infty)\to [0,\infty)$ be a differentiable convex function with $f(0)=0$. We prove that $$f^{\prime}(0)(A \sigma B)\leq…

We demonstrate new abstract characterizations for unital and non-unital operator spaces. We characterize unital operator spaces in terms of the cone of accretive operators (operators whose real part is positive). Defining the gauge of an…

This research includes the study of some positive sampling Kantorovich operators (SK operators) and their convergence properties. A comprehensive analysis of both local and global approximation properties is presented using sampling…

Let f be a non-negative concave function on the positive half-line. Let A and B be two positive matrices. Then, for all symmetric norms, || f(A+B) || is less than || f(A)+f(B) ||. When f is operator concave, this was proved by Ando and…

In this article, we proved upper bounds for numerical radius of bounded linear operator and product of operators which generalize and improve existing inequalities. We also obtain a numerical radius inequality of invertible operator using…

In this paper we introduce the concept of quadratic operator perspective for a continuous function {\Phi} defined on the positive semi-axis of real numbers. This generalize the quadratic weighted operator geometric mean and the quadratic…

We consider positive, integral-preserving linear operators acting on $L^1$ space, known as stochastic operators or Markov operators. We show that, on finite-dimensional spaces, any stochastic operator can be approximated by a sequence of…

We obtain limit theorems for $\Phi(A^p)^{1/p}$ and $(A^p\sigma B)^{1/p}$ as $p\to\infty$ for positive matrices $A,B$, where $\Phi$ is a positive linear map between matrix algebras (in particular, $\Phi(A)=KAK^*$) and $\sigma$ is an operator…

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…

Several matrix/operator inequalies are given. Most of them are unexpected extensions of the Araki Log-majorization theorem, obtained thanks to a new log-majorization for positive linear maps and normal operators (Theorem 2.9). The main idea…

We present several Ando-Hiai type inequalities for $n$-variable operator means for positive invertible operators. Ando-Hiai's inequalities given here are not only of the original type but also of the complementary type and of the reverse…

We prove that a continuous function $f:(0,\infty) \to (0,\infty)$ is operator monotone increasing if and only if $f(A \: !_t \: B) \leqs f(A) \: !_t \: f(B)$ for any positive operators $A,B$ and scalar $t \in [0,1]$. Here, $!_t$ denotes the…