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Jamal Rooin

Publications and source records attributed to Jamal Rooin.

8 recordsLinked to original sources
arXiv2020

Homomorphisms of C*-algebras and their K-theory

Let $A$ and $B$ be C*-algebras and $φ\colon A\to B$ be a $*$-homomorphism. We discuss the properties of the kernel and (co-)image of the induced map $\mathrm{K}_{0}(φ)\colon \mathrm{K}_{0}(A) \to \mathrm{K}_{0}(B)$ on the level of K-theory. In particular, we are interested in the case that the co-image is torsion free, and show that it holds when $A$ and $ B $ are commutative and unital, $B$ has real rank zero, and $φ$ is unital and injective. We also show that $ A$ is embeddable in $B$ if $ \mathrm{K}_{0}(φ)$ is injective and $A$ has stable rank one and real rank zero.

math.OA↗
arXiv2018

Operator revision of a Ky Fan type inequality

Let $\mathscr{H}$ be a complex Hilbert space and $A,B\in \mathbb{B}(\mathscr{H})$ such that $0<A,B\leq\frac{1}{2}I$. Setting $A':=I-A$ and $B':=I-B$, we prove $$ A'\nabla_λB'-A'!_λB' \leq A\nabla_λB-A!_λB, $$ where $\nabla_λ$ and $!_λ$ denote the weighted arithmetic and harmonic operator means, respectively. This inequality is the natural extension of a Ky Fan type inequality due to H. Alzer. Some parallel and related results are also obtained.

math.FA↗
arXiv2013

Some Monotonicity Properties of Convex Functions with Applications

We mainly establish a monotonicity property between some special Riemann sums of a convex function $f$ on $[a,b]$, which in particular yields that $\frac{b-a}{n+1}\sum_{i=0}^n f\left(a+i\frac{b-a}{n}\right)$ is decreasing while $\frac{b-a}{n-1}\sum_{i=1}^{n-1} f\left(a+i\frac{b-a}{n}\right)$ is an increasing sequence. These give us a new refinement of the Hermitt-Hadamard inequality. Moreover, we give a refinement of the classical Alzer's inequality together with a suitable converse to it. Applications regarding to some important convex functions are also included.

math.CA↗
arXiv2007

An Extension of Alzer's Inequality

In this article, we obtain two interesting general inequalities concerning Riemman sums of convex functions, which in particular, sharpen Alzer's inequality and give a suitable converse for it.

math.CA↗
arXiv2007

Some New Inequalities Between Important Means

In this paper, mainly using the convexity of the function $\frac{a^x-b^x}{c^x-d^x}$ and convexity or concavity of the function $\ln\frac{a^x-b^x}{c^x-d^x}$ on the real line, where $a>b\geq c>d>0$ are fixed real numbers, we obtain some important relations between various important means of these numbers. Also, we apply the obtained results to Ky Fan type inequalities and get some new refinements.

math.CA↗