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Amir Ghasem Ghazanfari

Publications and source records attributed to Amir Ghasem Ghazanfari.

6 recordsLinked to original sources
arXiv2023

An extension of the weighted geometric mean in unital $JB$-algebras

Let $\mathcal{A}$ be a unital $JB$-algebra and $A,~B\in\mathcal{A}$, we extend the weighted geometric mean $A\sharp_r B$, from $r\in [0,1]$ to $r\in (-1, 0)\cup(1, 2)$. We will notice that many results will be reversed when the domain of $r$ change from $[0,1]$ to $(-1,0)$ or $(1,2)$. We investigate some property of $A\sharp_r B$ for such quantities of $r$, such as we show that $A\sharp_r B$ is separately operator convex with respect to $A, B$. We also introduce the Heinz and Heron means for unital $JB$-algebras and give some famous inequalities involving them.

math.FA↗
arXiv2021

Norm inequalities related to operator monotone functions

Let $A$ be a positive definite operator on a Hilbert space $H$, and $|||.|||$ be a unitarily invariant norm on $B(H)$. We show that if $f$ is an operator monotone function on $(0,\infty)$ and $n\in \mathbb{N}$, then $|||D^n f(A)|||\leq\|f^{(n)}(A)\|$ and $\|f^{(n)}(\cdot)\|$ is a quasi-convex function on the set of all positive definite operators in $B(H)$. We establish some estimates of the right hand side of some Hermite-Hadamard type inequalities in which differentiable functions are involved, and norms of the maps induced by them on the set of self adjoint operators are convex, quasi-convex or $s$-convex. As applications, we obtain some of bounds for $|||f(B)-f(A)|||$ in term of $|||B-A|||$. For instance, Let $f,g$ be two operator monotone functions on $(0,\infty)$. Then, for every unitarily invariant norm $|||.|||$ and every positive definite operators $A,B$, \begin{align*} &\left|\left|\left|f(A)g(A)-f(B)g(B)\right|\right|\right|\notag\\ &\leq|||B-A|||\Big[\max\left\{\|f'(A)\|,\|f'(B)\|\right\}\times\max\left\{\|g(A)\|,\|g(B)\|\right\}\notag\\ &+\max\left\{\|f(A)\|,\|f(B)\|\right\}\times \max\left\{\|g'(A)\|,\|g'(B)\|\right\}\Big]. \end{align*}

math.FA↗
arXiv2020

Refined Heinz operator inequalities and norm inequalities

In this article we study the Heinz and Hermite-Hadamard inequalities. We derive the whole series of refinements of these inequalities involving unitarily invariant norms, which improve some recent results, known from the literature. We also prove that if $A , B, X\in M_n(\mathbb{C})$ such that $A$ and $B$ are positive definite and $f$ is an operator monotone function on $(0,\infty)$. Then \begin{equation*} |||f(A)X-Xf(B)|||\leq \max\{||f'(A)||, ||f'(B)||\} |||AX-XB|||. \end{equation*} Finally we obtain a series of refinements of the Heinz operator inequalities, which were proved by Kittaneh and Krnić.

math.FA↗
arXiv2019

Some Gruss type inequalities for Frechet differentiable mappings

Let X be a Hilbert C^*-module on C^*-algebra A and p in A. We denote by Dp(A;X) the set of all continuous functions f on A, which are Frechet differentiable on a open neighborhood U of p. Then, we introduce some generalized semi-inner products on Dp(A;X), and using them some Gruss type inequalities in semi-inner product C^*-module Dp(A;X) and Dp(A;X^n) are established.

math.FA↗