M. Kian

activity

20132026

2 \times 2

block matrices of operators

48 citations · 73 across the 25 of their papers we have counts for

collaborators

30 papers

math-ph2026

Operator Schmidt Rank and the Geometry of Schmidt Profiles

Mohsen Kian, Mohammad Sal Moslehian

The main result of the paper states that if $0 \neq = v \in C^{m} \otimes C^{n}$ , $d = min {m, n}$ , and $p = S R (v)$ , then for every $1 \leq q \leq d$ , \begin{equation*} \min\left\{OS…

math.OA2026

Minimal Wittstock Envelopes of Hermitian Completely Bounded Maps

Mohsen Kian

A Hermitian completely bounded map $Φ : A \to B (H)$ need not have a canonical completely positive analogue of an absolute value. We study this problem through the…

math.FA2026

Sharpness Loss for Radon--Nikodym Derivatives of Completely Positive Maps

Mohsen Kian

The Radon--Nikodym theorem for completely positive maps identifies the order interval below a map with positive contractions in the commutant of its minimal Stinespring representat…

math-ph2026

Finite-Corner Reconstruction and Separation for Cones of Normal Maps

Mohsen Kian, Fuad Kittaneh

We develop a finite-corner framework for convex cones of normal maps between $\mathcal B(\mathcal H)$ and $\mathcal B(\mathcal K)$. The basic structural assumption is stability…

math.OA2026

Relative Kubo-Ando Means of Completely Positive Maps

Mohsen Kian

We develop a Kubo--Ando theory on order intervals of completely positive maps. Using Arveson's Radon--Nikodym theorem as a structural tool, we define relative Kubo--Ando means \(Φσ…

quant-ph2026

Kubo-Ando Means and Rigidity of Quantum Positivity Cones

Mohsen Kian

We investigate the stability of quantum positivity cones under nonlinear operator means. Specifically, we examine how Kubo--Ando means interact with the separable, positive partial…

math.FA2026

Fractional $k$ -positivity: a continuous refinement of the $k$ -positive scale

Mohsen Kian

We introduce a real-parameter refinement of the classical integer hierarchies underlying Schmidt number, block-positivity, and $k$ -positivity for maps between matrix algebras. Star…

math.OA2025

Matrix-Test Duality: A Support-Function Characterization for $C^{*}$ -Convex Families of CP Maps

Mohsen Kian, Mario Krnic

We develop a matrix-test dual framework for $C^{*}$ -convex families of completely positive maps $\CP(\mathscr S,\mathscr T)$, where $S$ is an operator system and $\mathscr T…

quant-ph2025

Sharp Asymptotics for $k$ -Positivity Shifts under Singular Perturbations

Mohsen Kian

We show that, as the Choi matrix of a completely positive perturbation direction approaches a singular limit, the shift required for $k$ -positivity can diverge more slowly than tha…

math.FA2024

Some Generalizations of Mercer inequality and its operator extensions

Mohsen Kian, Zainab Peymani Mazraj

We study the Mercer inequality and its operator extension for superquadratic functions. In particular, we give a more general form of the Mercer inequality by replacing some consta…

math.FA2023

Improved eigenvalue inequalities via two major subclasses of superquadratic functions

Mohsen Kian

There exist two major subclasses in the class of superquadratic functions, one comprises concave and decreasing functions, while the other consists of convex and monotone increasin…

math.FA2023

Matrix Inequalities between $f (A) σ f (B)$ and $A σ B$

Manisha Devi, Jaspal Singh Aujla, Mohsen Kian +1

Let $A$ and $B$ be $n \times n$ positive definite complex matrices, let $σ$ be a matrix mean, and let $f : [0, \infty) \to [0, \infty)$ be a differentiable convex function with $f(0)=…

quant-ph2023

A new estimation of the quantum Chernoff bound

Mohsen Kian, Trung Hoa Dinh, Mohammad Sal Moslehian +1

Relating to finding possible upper bounds for the probability of error for discriminating between two quantum states, it is well-known that \begin{align*} \mathrm{tr}(A+B) - \mathr…

math.OA2022★ 6 cited

Decomposition of tracial positive maps and applications in quantum information

Ali Dadkha, Mohsen Kian, Mohammad Sal Moslehian

Every positive multilinear map between $C^{*}$ -algebras is separately weak $^{*}$ -continuous. We show that the joint weak $^{*}$ -continuity is equivalent to the joint weak $^{*}$ -continuity o…

cs.IT2021★ 1 cited

How type of Convexity of the Core function affects the Csiszár $f$ -divergence functional

Mohsen Kian

We investigate how the type of Convexity of the Core function affects the Csiszár $f$ -divergence functional. A general treatment for the type of convexity has been considered and t…

math.FA2020★ 1 cited

Jointly convex mappings related to the Lieb's functional and Minkowski type operator inequalities

Mohsen Kian, Yuki Seo

Employing the notion of operator log-convexity, we study joint concavity $/$ convexity of multivariable operator functions: $(A, B) \mapsto F (A, B) = h [Φ (f (A)) σ Ψ (g (B))]$ ,…

math.FA2020

Klein's trace inequality and superquadratic trace functions

Mohsen Kian, Mohammad W. Alomari

We show that if $f$ is a non-negative superquadratic function, then $A \mapsto Tr f (A)$ is a superquadratic function on the matrix algebra. In particular, \begin{align*} \tr…

math.FA2020★ 6 cited

Asymmetric Choi--Davis inequalities

Mohsen Kian, M. S. Moslehian, R. Nakamoto

Let $Φ$ be a unital positive linear map and let $A$ be a positive invertible operator. We prove that there exist partial isometries $U$ and $V$ such that \[ |Φ(f(A))Φ(A)Φ(g(A))|\le…

math.FA2019

Matricial Radius: A Relation of Numerical radius with Matricial Range

Mohsen Kian, Mahdi Dehghani, Mostafa Sattari

It has been shown that if $T$ is a complex matrix, then {\small\begin{align*} ω(T)&=\frac{1}{n}\sup\left\{|\mathrm{Tr}\ X|;\ X\in W^n(T)\right\}\\ &=\frac{1}{n}\sup\left\{\|X\|_1;\…

math.FA2019★ 1 cited

Variants of Ando--Hiai type inequalities for deformed means and applications

Mohsen Kian, M. S. Moslehian, Yuki Seo

For an $n$ -tuple of positive invertible operators on a Hilbert space, we present some variants of Ando--Hiai type inequalities for deformed means from an $n$ -variable operator mean…

math.FA2019★ 48 cited

Positivity of $2 \times 2$ block matrices of operators

Mohammad Sal Moslehian, Mohsen Kian, Qingxiang Xu

We review some of the significant generalizations and applications of the celebrated Douglas theorem on the equivalence of factorization, range inclusion, and majorization of opera…

math.FA2018

Power means of probability measures and Ando-Hiai inequality

Mohsen Kian, Mohammad Sal Moslehian

Let $μ$ be a probability measure of compact support on the set $P_{n}$ of all positive definite matrices, let $t \in (0, 1]$ , and let $P_{t} (μ)$ be the unique positive solution o…

math.FA2018

Interpolating operator Jensen-type inequalities for log-convex and superquadratic functions

Mojtaba Bakherad, Mohsen Kian, Mario Krnic +1

Motivated by some recently established operator Jensen-type inequalities related to a usual convexity, in the present paper we derive several more accurate operator Jensen-type ine…

math.FA2017

A refinement of Hardy Inequality via superquadratic function

Mohsen Kian, M. Rostamian Delavar

A refinement of the Hardy inequality has been presented by use of superquadratic function.

Operator Schmidt Rank and the Geometry of Schmidt Profiles

Minimal Wittstock Envelopes of Hermitian Completely Bounded Maps

Sharpness Loss for Radon--Nikodym Derivatives of Completely Positive Maps

Finite-Corner Reconstruction and Separation for Cones of Normal Maps

Relative Kubo-Ando Means of Completely Positive Maps

Kubo-Ando Means and Rigidity of Quantum Positivity Cones

Fractional k-positivity: a continuous refinement of the k-positive scale

Matrix-Test Duality: A Support-Function Characterization for C∗-Convex Families of CP Maps

Sharp Asymptotics for k-Positivity Shifts under Singular Perturbations

Some Generalizations of Mercer inequality and its operator extensions

Improved eigenvalue inequalities via two major subclasses of superquadratic functions

Matrix Inequalities between f(A)σf(B) and AσB

A new estimation of the quantum Chernoff bound

Decomposition of tracial positive maps and applications in quantum information

How type of Convexity of the Core function affects the Csiszár f-divergence functional

Jointly convex mappings related to the Lieb's functional and Minkowski type operator inequalities

Klein's trace inequality and superquadratic trace functions

Asymmetric Choi--Davis inequalities

Matricial Radius: A Relation of Numerical radius with Matricial Range

Variants of Ando--Hiai type inequalities for deformed means and applications

Positivity of 2×2 block matrices of operators

Power means of probability measures and Ando-Hiai inequality

Interpolating operator Jensen-type inequalities for log-convex and superquadratic functions

A refinement of Hardy Inequality via superquadratic function

Fractional $k$ -positivity: a continuous refinement of the $k$ -positive scale

Matrix-Test Duality: A Support-Function Characterization for $C^{*}$ -Convex Families of CP Maps

Sharp Asymptotics for $k$ -Positivity Shifts under Singular Perturbations

Matrix Inequalities between $f (A) σ f (B)$ and $A σ B$

How type of Convexity of the Core function affects the Csiszár $f$ -divergence functional

Positivity of $2 \times 2$ block matrices of operators